'New' build failure

I built a new system and moved the old MB/Ram/Video/CPU/PSU to a another
case with the Hard Drives from another system that died. The new system
works fine, but the moved parts won't boot up. I get to the boot screen, but
I can't get into the BIOS. The Num Lock on the Keyboard seems to work fine
at first, but then gets flakier as time goes on. The Caps Lock key does not
function at all. This keyboard was working fine when I was testing the new
build. The only thing I did to the moved parts was replace the CPU cooler.
My first thought is a CPU problem, but the system powers up and Resets fine.
Maybe a power issue?

So where to start looking?