With an intermittent issue like that, I'm leaning towards hardware myself. Power supply, hard drive, RAM, in that order I'd say.

If you have a standard multimeter you can check how many volts your PSU is putting out - it should be within 10%. Unfortunately that test does not properly load-test the power supply, but assuming you test voltage with the computer powered on that should be a start. I'd test from an unused 4-pin Molex connectors - you should get 5v and 12v from those. Do NOT try to measure Amps using a multimeter unless you know what you're doing, that will likely short out the power supply and - at best - pop the fuse in the multimeter without further damage, and at worst could start a fire.

Hard drive, try and get the SMART data from it. Even if the software says it passes, look for things like Load Cycle and see if they're excessively high (over 300,000).

Ram - load Memtest86 onto a USB stick and run that overnight until it passes at least 3 times with no failure. It's possible for inconsistent RAM to pass, hence going for at least 3 passes. Leave it for a few days if you like.

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