Computer shuts off a few seconds only if hard drives are plugged in

Hello,
I have a problem with my computer, you press the power and it seems to come on, but does not beep or post i think it is..but rather just shuts off.
If i want to try again to turn it on, i must pull the power/or switch off on back for few seconds, then try again; but it is the same result.
If i unplug the power to the hard drive, only then does it boot up (posts) but then I have no hard drive.
Any idea what could be going on here.? CD roms plugged in, but with hard drives plugged in, no success. This just started happening...the computer just won't power up to boot up now, just shuts off after about 3 seconds after pressing switch on front.

Could it be power supply, i get the light on the motherboard. ..and like i said witout harddrives plugged into power, it seems to be ok.

any help is appreciated
thank you
KC