I have seen this before on some machines. Althought your power supply does seem really, really low on your 2nd machine. only 450? And you are running a C2Q with a 9600gt???
If you do not even get the BIOS post screen, you will not be able to try the things people have suggested. If there is no POST, it is not software.
I would do what LordB said and reset the CMOS.
If this doesn't work, take all peripherals except 1 stick of RAM, CPU, and 1 Video card (no sli) out. And try booting. Work your way up.
Again, your 2nd machine's power supply it very, very low. I am surprised you had the right power rails to power the 9600gt. Did you use adapters?
as usasma has suggested, i have seen some machines go in to a sleep mode that they could not get out of, but a CMOS reset and total power drain usually fixed this (Power down machine, pull the plug, the hit the power button repeatedly to discharge the power)