Dying PSU or mobo?

I've got a computer that doesn't power up occasionally. I'll press the power button and nothing will happen. Then if I keep repeatedly pressing the power button, sooner or later it'll power on. It can literally take 200 button presses before it finally powers up. Once it boots and loads up Windows, it seems to run fine and I can leave it running for days without any hiccups.

I've tried using a paper clip to try and turn on the computer while bypassing the power switch on the computer and it didn't seem to make much difference. Just to be on the safe side, I moved everything from the current case to a new case so I could be sure about ruling out a bad switch. Still had the intermittent problem and when it did power up, everything ran fine in the new case too.

So I'm wondering if it's a PSU on it's last legs or if it's the mobo? The mobo is an Asus A8V-Deluxe (socket 939) and it's getting on in years. PSU is the Antec one included in the first Antec Sonata cases. I believe it's a 300W model. It's plugged into a UPS unit as well. Tried bypassing the UPS but still had the same issue with not starting sometimes.

Should I get a new PSU and see if that fixes the problem? I guess if the new unit doesn't change things then it's most likely a bad mobo?

Any help would be appreciated.

Changing the power supply first is the simpler cheaper option; however sod’s law says that it is probably the motherboard.