My mom has an eMachine ET1161-05 (I know, it's junk as it is.) It recently started having a problem. It would turn on, show the BIOS options for a few seconds, then freeze up, the display and LEDs would stay but nothing happened, Numlock and Capslock didn't make the other LEDs turn on. There is about a 4% chance that it will boot normally and work all day. I did a GPU, RAM, and CPU stress test. All were ran for their recommended times, it came back with no errors. Can somebody confirm that this is a motherboard error?
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Unfortunately, the only way to verify a bad motherboard is to substitute a known good one. And if you cannot get another motherboard of the same type, you will probably need to rebuild your OS.