Computer wont boot after losing power

I had an issue recently where my computer wouldn't boot unless I jumped the motherboard using a paper clip to connect the green and black cables on the 24-pin slot on the motherboard. Ultimately, loading the fail-safe bios and using optimized settings, I was able to get the computer to boot without the jumper.

However, should I flip the switch in the back or unplug the computer (say if I was taking the computer to a LAN party or something) it won't boot and I need to jump the motherboard again. Yes, everything is plugged in and properly seated. I've been trying to get this computer working for weeks and this last bit really boggles my mind. I've been going back and forth with Gigabyte's customer support, which helped with previous problems, but I'm really hoping I can get a better answer faster here.

Thanks in advance. Everyone at Tom's has been really helpful every time I've used it.

Edit:
Gigabyte MA790FXT-UD5P
AMD Phenom II x3
4GB Crucial Ballistic RAM
500W Corsair power supply
40GB Western Digital Hard drive
Nvidia 9800GTX+ Black Edition
New Wireless Adapter

Also, if it makes a difference, I put in a new motherboard battery.