that this problem may very well be a hardware-thing.
I read somewhere on the Dell userforum (Yes, Dell has one on their website somewhere; look for 'community' or that sort of thing) that the C-line of machines are designed wrong somewhere around the CPU socket. This CPU module form factor thing is called MMC1 or similar. I recall something about a clip, intended to hold the CPU in place but unabnle to do this properly by design. Dell seemed to be aware of the problem as customers were able to request new clips at no charge.
Have a couple of these C-series wrecks lying around, both completely dead like yours. Haven't had time to tinker with them yet, but this is where i'd start; poking at the cpu-socket-thingy.
BTW: C's with no memory installed respond to powerbutton by blinking their led's a few times, then completely shutting off again - no screen activity at all.
HD absent is not a problem. A working C-model will boot fine without it - and ask for boot media
Good luck!