Gfilui

NUC model: NUC7i3BNK
OS: Lubuntu 14.04.2
Kernel: 3.13.0-53

contents of /etc/network/interfaces:

auto lo
iface lo inet loopback

auto eth0
iface eth0 inet dhcp

ifconfig -a:

lo Link encap:Local Loopback 
 inet addr:127.0.0.1 Mask:255.0.0.0
 inet6 addr: ::1/128 Scope:Host
 UP LOOPBACK RUNNING MTU:65536 Metric:1
 RX packets:2115 errors:0 dropped:0 overruns:0 frame:0
 TX packets:2115 errors:0 dropped:0 overruns:0 carrier:0
 collisions:0 txqueuelen:0 
 RX bytes:151791 (151.7 KB) TX bytes:151791 (151.7 KB)

lspci -v: 

00:00.0 Host bridge: Intel Corporation Device 5904 (rev 02)
 Subsystem: Intel Corporation Device 2068
 Flags: bus master, fast devsel, latency 0
 Capabilities: [e0] Vendor Specific Information: Len=10 <?>

00:02.0 VGA compatible controller: Intel Corporation Device 5916 (rev 02) (prog-if 00 [VGA controller])
 Subsystem: Intel Corporation Device 2068
 Flags: bus master, fast devsel, latency 0, IRQ 11
 Memory at db000000 (64-bit, non-prefetchable) [size=16M]
 Memory at 90000000 (64-bit, prefetchable) [size=256M]
 I/O ports at f000 [size=64]
 Expansion ROM at <unassigned> [disabled]
 Capabilities: [40] Vendor Specific Information: Len=0c <?>
 Capabilities: [70] Express Root Complex Integrated Endpoint, MSI 00
 Capabilities: [ac] MSI: Enable- Count=1/1 Maskable- 64bit-
 Capabilities: [d0] Power Management version 2
 Capabilities: [100] #1b
 Capabilities: [200] Address Translation Service (ATS)
 Capabilities: [300] #13

00:08.0 System peripheral: Intel Corporation Device 1911
 Subsystem: Intel Corporation Device 2068
 Flags: bus master, fast devsel, latency 0, IRQ 11
 Memory at dc24f000 (64-bit, non-prefetchable) [size=4K]
 Capabilities: [90] MSI: Enable- Count=1/1 Maskable- 64bit-
 Capabilities: [dc] Power Management version 2
 Capabilities: [f0] PCI Advanced Features

00:14.0 USB controller: Intel Corporation Device 9d2f (rev 21) (prog-if 30 [XHCI])
 Subsystem: Intel Corporation Device 2068
 Flags: bus master, medium devsel, latency 0, IRQ 136
 Memory at dc230000 (64-bit, non-prefetchable) [size=64K]
 Capabilities: [70] Power Management version 2
 Capabilities: [80] MSI: Enable+ Count=1/8 Maskable- 64bit+
 Kernel driver in use: xhci_hcd

00:14.2 Signal processing controller: Intel Corporation Device 9d31 (rev 21)
 Subsystem: Intel Corporation Device 2068
 Flags: bus master, fast devsel, latency 0, IRQ 11
 Memory at dc24e000 (64-bit, non-prefetchable) [size=4K]
 Capabilities: [50] Power Management version 3
 Capabilities: [80] MSI: Enable- Count=1/1 Maskable- 64bit-

00:16.0 Communication controller: Intel Corporation Device 9d3a (rev 21)
 Subsystem: Intel Corporation Device 2068
 Flags: bus master, fast devsel, latency 0, IRQ 11
 Memory at dc24d000 (64-bit, non-prefetchable) [disabled] [size=4K]
 Capabilities: [50] Power Management version 3
 Capabilities: [8c] MSI: Enable- Count=1/1 Maskable- 64bit+

00:17.0 SATA controller: Intel Corporation Device 9d03 (rev 21) (prog-if 01 [AHCI 1.0])
 Subsystem: Intel Corporation Device 2068
 Flags: bus master, 66MHz, medium devsel, latency 0, IRQ 138
 Memory at dc248000 (32-bit, non-prefetchable) [size=8K]
 Memory at dc24c000 (32-bit, non-prefetchable) [size=256]
 I/O ports at f090 [size=8]
 I/O ports at f080 [size=4]
 I/O ports at f060 [size=32]
 Memory at dc24b000 (32-bit, non-prefetchable) [size=2K]
 Capabilities: [80] MSI: Enable+ Count=1/1 Maskable- 64bit-
 Capabilities: [70] Power Management version 3
 Capabilities: [a8] SATA HBA v1.0
 Kernel driver in use: ahci

00:1c.0 PCI bridge: Intel Corporation Device 9d10 (rev f1) (prog-if 00 [Normal decode])
 Flags: bus master, fast devsel, latency 0
 Bus: primary=00, secondary=01, subordinate=39, sec-latency=0
 I/O behind bridge: 00002000-00002fff
 Memory behind bridge: c4000000-da0fffff
 Prefetchable memory behind bridge: 00000000a0000000-00000000c1ffffff
 Capabilities: [40] Express Root Port (Slot+), MSI 00
 Capabilities: [80] MSI: Enable- Count=1/1 Maskable- 64bit-
 Capabilities: [90] Subsystem: Intel Corporation Device 2068
 Capabilities: [a0] Power Management version 3
 Capabilities: [100] Advanced Error Reporting
 Capabilities: [140] Access Control Services
 Capabilities: [220] #19
 Kernel driver in use: pcieport

00:1c.5 PCI bridge: Intel Corporation Device 9d15 (rev f1) (prog-if 00 [Normal decode])
 Flags: bus master, fast devsel, latency 0
 Bus: primary=00, secondary=3a, subordinate=3a, sec-latency=0
 Memory behind bridge: dc100000-dc1fffff
 Capabilities: [40] Express Root Port (Slot+), MSI 00
 Capabilities: [80] MSI: Enable- Count=1/1 Maskable- 64bit-
 Capabilities: [90] Subsystem: Intel Corporation Device 2068
 Capabilities: [a0] Power Management version 3
 Capabilities: [100] Advanced Error Reporting
 Capabilities: [140] Access Control Services
 Capabilities: [200] L1 PM Substates
 Capabilities: [220] #19
 Kernel driver in use: pcieport

00:1c.7 PCI bridge: Intel Corporation Device 9d17 (rev f1) (prog-if 00 [Normal decode])
 Flags: bus master, fast devsel, latency 0
 Bus: primary=00, secondary=3b, subordinate=3b, sec-latency=0
 Memory behind bridge: dc000000-dc0fffff
 Capabilities: [40] Express Root Port (Slot+), MSI 00
 Capabilities: [80] MSI: Enable- Count=1/1 Maskable- 64bit-
 Capabilities: [90] Subsystem: Intel Corporation Device 2068
 Capabilities: [a0] Power Management version 3
 Capabilities: [100] Advanced Error Reporting
 Capabilities: [140] Access Control Services
 Capabilities: [200] L1 PM Substates
 Capabilities: [220] #19
 Kernel driver in use: pcieport

00:1f.0 ISA bridge: Intel Corporation Device 9d4e (rev 21)
 Subsystem: Intel Corporation Device 2068
 Flags: bus master, medium devsel, latency 0

00:1f.2 Memory controller: Intel Corporation Device 9d21 (rev 21)
 Subsystem: Intel Corporation Device 2068
 Flags: bus master, fast devsel, latency 0
 Memory at dc244000 (32-bit, non-prefetchable) [size=16K]

00:1f.3 Audio device: Intel Corporation Device 9d71 (rev 21) (prog-if 80)
 Subsystem: Intel Corporation Device 2068
 Flags: bus master, fast devsel, latency 32, IRQ 11
 Memory at dc240000 (64-bit, non-prefetchable) [size=16K]
 Memory at dc220000 (64-bit, non-prefetchable) [size=64K]
 Capabilities: [50] Power Management version 3
 Capabilities: [60] MSI: Enable- Count=1/1 Maskable- 64bit+

00:1f.4 SMBus: Intel Corporation Device 9d23 (rev 21)
 Subsystem: Intel Corporation Device 2068
 Flags: medium devsel, IRQ 11
 Memory at dc24a000 (64-bit, non-prefetchable) [size=256]
 I/O ports at f040 [size=32]

00:1f.6 Ethernet controller: Intel Corporation Device 15d8 (rev 21)
 Subsystem: Intel Corporation Device 2068
 Flags: bus master, fast devsel, latency 0, IRQ 11
 Memory at dc200000 (32-bit, non-prefetchable) [size=128K]
 Capabilities: [c8] Power Management version 3
 Capabilities: [d0] MSI: Enable- Count=1/1 Maskable- 64bit+
 Capabilities: [e0] PCI Advanced Features

3a:00.0 Network controller: Intel Corporation Device 24fd (rev 78)
 Subsystem: Intel Corporation Device 9010
 Flags: bus master, fast devsel, latency 0, IRQ 10
 Memory at dc100000 (64-bit, non-prefetchable) [size=8K]
 Capabilities: [c8] Power Management version 3
 Capabilities: [d0] MSI: Enable- Count=1/1 Maskable- 64bit+
 Capabilities: [40] Express Endpoint, MSI 00
 Capabilities: [100] Advanced Error Reporting
 Capabilities: [140] Device Serial Number 28-c6-3f-ff-ff-ae-5c-31
 Capabilities: [14c] Latency Tolerance Reporting
 Capabilities: [154] L1 PM Substates

3b:00.0 Unassigned class [ff00]: Realtek Semiconductor Co., Ltd. RTS5229 PCI Express Card Reader (rev 01)
 Subsystem: Intel Corporation Device 2068
 Flags: bus master, fast devsel, latency 0, IRQ 137
 Memory at dc000000 (32-bit, non-prefetchable) [size=4K]
 Capabilities: [40] Power Management version 3
 Capabilities: [50] MSI: Enable+ Count=1/1 Maskable- 64bit+
 Capabilities: [70] Express Endpoint, MSI 00
 Capabilities: [100] Advanced Error Reporting
 Capabilities: [140] Device Serial Number 00-00-00-01-00-4c-e0-00
 Kernel driver in use: rtsx_pci

I'm assuming that this is a driver issue, but I'm not sure how to resolve. The device cannot connect via wireless and cannot use Network Manager.

Thanks in advance!

The most hassle-free option will be to upgrade to Ubuntu 16.10 or later. If this is not an option for you, the following has been purported to work, but I can't personally speak to how well it works.

You will need to manually install firmware for the NUC7i3BNK, since it's not included in the Ubuntu 14.04 or 16.04 repositories. A guide for doing so can be found here: Ubuntu 16.04.2 on Intel NUC7i3, Bluetooth not working

Additionally, your kernel might not have drivers compiled in for that adapter. To fix this, you would have to recompile your kernel from source, which is a non-trivial undertaking, but also not too difficult, once you get the hang of it. (It's very CPU-intensive, and will take a few hours, most likely.) When you do the "xconfig" step, you'll need to locate the driver for your card and choose the option to compile it into the kernel. You can instead choose to compile the driver as a module, but then you'd have to load that module at boot by placing its name in /etc/modules. Unfortunately, I don't know what the name of that specific driver is, so you'll need to figure that out.

Here is a guide for recompiling your kernel:
What's a simple way to recompile the kernel?

Good luck!