New build - problem booting

I am building a new PC.

Casecom LG-7780 Black/Silver Gaming Case - With 350W PSU
AMD Athlon 64 (ADA3700DAA5BN) 3700 CPU Skt 939 San Diego
1GB DDR PC3200 400MHz 184pin Extra Value Ram
Maxtor 6V200E0 200GB SATA300 7200rpm 8MB Cache
ECS RD480-A939 Socket 939 Crossfire RD480 PCI-E x 2 DDR400 8channel audio ATX
LITEON DVD8900/DW1670 16x DVDRW/RAM Bare Black
Asus Nvidia 7300GS 256MB PCI-E

I booted the new system but after switching the on/off power switch on the PSU (back of the case), the CPU fan starts and I can see the power and HD LEDs lighting up on the front of the case. It does that for about 3 secs then powers off. I didn't have to press the on/off button on the case at this point... That is unexpected.

The mobo comes with a 24 pin power conector (4 of them covered by a yellow sticker with 24 pin written on it), an auxiliary 12V 4 pin power connector and it has a power socket that looks like the ones you use to power a DVD drive called ATX4P1.

The case however provides only a 20 pin ATX power connector not a 24 pin one.

I double checked how I connected all the front end panel wires (HD, PWR switch, HD LED etc) and they seem fine.

I don't know if it is something to do with connecting it to a 20 pin power connector or maybe the mobo is dead... Do I have to connect the one with 4 pins in the main power socket on the mobo instead of the 12V one?!

This is the first time I am building a system and am so nervous I did something wrong.