iMac keeps crashing and not starting back up again easily

I recently transported my iMac back to my parents house and since then it has been randomly crashing and turning itself off. It will turn back on but only if I hold the power button down for 10 seconds, wait a few minutes then turn it on again as normal. Before it turns off the screen freezes for 30 seconds then goes black.

This has happened several times and comes without warning.

I'm not sure what to do or if this is a problem I can fix myself.