Most of the older ATX power supplies only have 1 12v rail, so they deliver full power off of any connection if only 1 connection is used. You're right that both of the black wires are grounds. Of the other 2, 1 is a 12v+ and the other is 5v+. The yellow wire should be the 12v+ and the black right next to it should be the 12v ground. If you have a volt meter, just measure voltage between each hot lead and one of the ground leads with the power supply turned on. That will tell you which is which for sure.
Good luck! As much as I enjoyed my car sub, turned home sub, it really took up way too much space and it was a pain having to turn the pc power supply on separately from the amp. What can I say, I love automation?