If you can't pinpoint the exact cause of the problem via error messages, the next step is usually to start removing hardware piece by piece and starting up the computer. Unplug one hard drive and try to power up. If nothing, try the other one.

Does the fan in your power supply spin? If absolutely nothing is happening at all when you try to power it up, that really points toward the power supply. Even if nothing else in your computer works, the fan in the power supply should spin if it's not dead.