Weird Pink Lines, Low Resolution, No Graphics Card

So...I recently (week or so ago) built a new computer. It booted up, I installed windows, steam, fraps, a few games, and some anti-virus. I even played a few hours of Just Cause 2, Witcher 2, and Assassin's Creed 3 with no problems. In fact, I played AC3 just last night with no problems. Consequently, you can imagine my suprise when I booted up my comp this morning and there were thick, pink lines across the screen. In addition, the resolution was set to 800x600 instead of my native 1920x1080. Finally, I could not get into the Nvidia control panel and dxdiag told me I had no video card plugged in.

To attempt to remedy my problem, I checked my drivers (all updated), restarted my computer, and took out and put back in my GPU.

A few hours on the internet revealed that this was probably a problem with my mobo or my GPU and that I'm probably gonna need to RMA one or the other. So, the question is, how to I figure out what is broken? Or, is there anything I can do at home to fix this?

System Specs:
Intel Core i5-2500K Sandy Bridge 3.3GHz (3.7GHz Turbo Boost) LGA 1155 95W Quad-Core Desktop Processor Intel HD Graphics 3000
GIGABYTE GA-Z77-DS3H LGA 1155 Intel Z77 HDMI SATA 6Gb/s USB 3.0 ATX Intel Motherboard
Rosewill BLACKHAWK Gaming ATX Mid Tower Computer Case, come with Five Fans, window side panel, top HDD dock
Rosewill Stallion Series RD500-2DB 500W ATX12V Power Supply
GeForce GTX 660, 2048MB GDDR5, HDMI, DVI-I, DVI-D, DP SLI Ready Video Card
Crucial Ballistix sport 8GB (2 x 4GB) 240-Pin DDR3 SDRAM DDR3 1600 (PC3 12800) Desktop Memory
Sony Optiarc 24X DVD Burner, Bulk Package 24X DVD+R 8X DVD+RW 12X DVD+R DL 24X DVD-R 6X DVD-RW 16X DVD-ROM 48X CD-R 32X CD-RW 48X CD-ROM Black SATA Model AD-7280S-0B - OEM
Seagate Barracuda ST1000DM003 1TB 7200 RPM 64MB Cache SATA 6.0Gb/s 3.5" Internal Hard Drive -Bare Drive

PS: When I unplugged my graphics card and used integrated graphics everything worked fine.