[Troubleshooting] Built computer but it won't turn on. Wrong power supply?

So this is my first build and I really hope I'll be able to figure this out. I have everything together and I don't think I ruined any part but it won't turn on. The case light comes on for about a second, the fans turn a bit, and then it turns off. My best guess is that I bought a power supply that doesn't work with the motherboard.

My power supply: Corsair 430W ATX12V Power Supply

My motherboard: Gigabyte GA Z77 DS3H 1155 ATX

My case: Rosewill Challenger ATX Midtower

There's an ATX 12V 4 pin (2x2) on the motherboard that has no connection and my power supply does not have cable that will fit that. Could that be my problem?

I'm going to bed soon but I figure I can post this tonight and then I can make more comments tomorrow too.