I have a Toshiba S55-A5236, currently I have Ubuntu 13.04 installed and my kernel 3.12.0-031200-generic. When I do lspci I get back:

00:00.0 Host bridge: Intel Corporation Haswell DRAM Controller (rev 06)

00:02.0 VGA compatible controller: Intel Corporation Haswell Integrated Graphics Controller (rev 06)

00:03.0 Audio device: Intel Corporation Haswell HD Audio Controller (rev 06)

00:14.0 USB controller: Intel Corporation Lynx Point USB xHCI Host Controller (rev 04)

00:16.0 Communication controller: Intel Corporation Lynx Point MEI Controller #1 (rev 04)

00:1a.0 USB controller: Intel Corporation Lynx Point USB Enhanced Host Controller #2 (rev 04)

00:1b.0 Audio device: Intel Corporation Lynx Point High Definition Audio Controller (rev 04)

00:1c.0 PCI bridge: Intel Corporation Lynx Point PCI Express Root Port #1 (rev d4)

00:1c.2 PCI bridge: Intel Corporation Lynx Point PCI Express Root Port #3 (rev d4)

00:1c.3 PCI bridge: Intel Corporation Lynx Point PCI Express Root Port #4 (rev d4)

00:1d.0 USB controller: Intel Corporation Lynx Point USB Enhanced Host Controller #1 (rev 04)

00:1f.0 ISA bridge: Intel Corporation Lynx Point LPC Controller (rev 04)

00:1f.2 SATA controller: Intel Corporation Lynx Point 6-port SATA Controller 1 [AHCI mode] (rev 04)

00:1f.3 SMBus: Intel Corporation Lynx Point SMBus Controller (rev 04)

02:00.0 Network controller: Realtek Semiconductor Co., Ltd. Device 8179 (rev 01)

03:00.0 Ethernet controller: Qualcomm Atheros QCA8171 Gigabit Ethernet (rev 10)

I am dual booting Windows 8.1 (not by my choice) and Ubuntu 13.04 (both are x64) Due to the latest kernel update I am now stuck without wifi and have been trying to fix it without any luck. If someone would please help me (and I am a beginner at bash, but eager to learn) fix this problem prior to me throwing this computer out the window I would be very grateful.

Oh, I have tried to download the driver from the website and compile it, but I am receiving compilation errors. I tried FreedomBen's git solution but I can figure it out.

Thanks,
Jack Dare

UPDATE:

user217298's answer was the fix, to why chili555's answer wouldn't work, however after the fix my wifi is now working. I would put a checkmark next to his answer but it wont let me.

Thank you for your answers.