More than likely the PSU, however:
you should do some tests first:
disconnect power to floppy and cr rom drives and maybe also take out your sound and modem cards etc, anything to reduce the power load.
If this solves your problem then either you need a bigger (or better) power supply, or possibly one of the devices/cables you removed/disconnected is faulty (you could easily test for this by swapping parts around).
You could also try unplugging everything (including your motherboard) and plugging it back in in case something is loose (and check for bad, dirty, or bent pins while you're at it).
I'd check your case temperature as well. If your machine is too hot then lots of strange things can start happening.
Symptoms of a dying PSU:
System restarts on its own
Spontaneously goes into standby
Fan does not run, runs slowly, or runs noisily
Computer is heating up
Dim display
Any number of different things. Almost all PSU symptoms are also symptoms of another failure. For instance, a dying PSU can cause lockups or invalid page faults or disconnections from the Internet.
Computer may not power on or may not complete PoST
Drives may not work intermittently
Multiple drives must be replaced repeatedly
Crackling audio
Computer running slowly
Drives intermittently not detected
If it's the PSU (more than likely), get a new one, a PSU on the way out could cause you some major headaches on your system.
