As Fisherking says a defective laptop is a lot trickier to both diagnose and troubleshoot.
Personally it sounds like a RAM or a power supply issue. Defective RAM is usually an easy fix in a laptop (one of the few removable parts). A power supply is many times worse. That said it could be a heat issue. My last pc was a laptop, when I replaced it with my current desktop I cracked it open, there was a a huge wad of compressed dust stuck in the fan and heat sink. Removing it (and increasing amount of RAM) solved the problems it had with being incredibly slow.
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