PSU might be dying, if it can't supply enough power to all the componetents perhaps it wasn't getting any to the CPU. Unplugging a cd-rom or hard drive would mean that power could go to the motherboard/cpu so it'd boot. Not sure why when you plug them back in it'll boot again, but I'd replace the PSU anyways just incase. A faulty PSU can give you all sorta of trouble and destroy components, and it's a relatively cheap fix.
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