It could be a failing power supply, but
here's a good article to help you diagnose the issue. A local computer technician will be able to load test your power supply if you take it in to them and let you know quickly if that is indeed the problem, in which case it's fairly inexpensive to remedy.
Otherwise I would guess a boot issue of some kind.
I hope this information allows you to resolve this issue. If you need further assistance, please post back with a comment to this thread.
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