I'm working on a friends iMac 1-gig 17in. machine and it has a very similar problem, it won't start unless I open the case and disconnect and reconnect something, almost anything, harddrive, DVD-drive, fan, power-supply, etc.
Once it starts it will start and restart all day long but if I turn off the power to the outlet (but leave the computer plugged in) it won't start the next morning.

This all sounds weird until we realize that probably all computers (including Apple and it's PMU (power management unit)) have something that controls all starting,restarting,sleeping,waking,and shutdown procedures.

I've had many PC's refuse to start until I removed, waited, and reinstalled slot installed components. Mac's don't generally suffer from this malady but I believe you and I have machines that have a leaky capacitor or some other faulty component (regardless of where it's located, motherboard, power-supply board, a bad stick of memory, or even a bad controller on the DVD drive) that's confusing or telling the PMU that there is some error and it should not start the machine.

If the problem is just a confused PMU it can be reset on a Mac by pushing the Cuda (PMU reset) switch (located in different places on different Mac motherboards) or remotely on some Macs (disconnect all cables and hold the power button while connecting the power cable then releasing and pressing it again. This is a good fix if there isn't a hardware problem but if there is the offending component will need to be diagnosed and replaced.

Which begs me to ask..... has any official Apple repair depot ever just replaced the fuse on a Mac power-supply board ($2.00 fuse + case cracking charge - Thank You Very Much!) or do they tell you the power supply is bad and they can install a reconditioned one for $300.00! And if they haven't then do they recondition yours (replace the fuse) and resell it to another sucker for $300 + parts and labor and whatever the traffic will bear?

Hope this helps a little and gives you a place to start.

-MrMac123