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In my experience, many problems involving unexpected reboots have to do with the computer’s RAM, or memory. It could be that you’ve got some bad memory or it may be some kind of incompatibility between manufacturers. With so many different makes and models and grades of RAM on the market, it is very easy to get the wrong kind for your motherboard, so double check what you have to make sure they will work together.
The easiest way to test computer memory is one stick at a time. If you only have one stick, try removing it from the slot and use compressed air to clean the connectors, then reseat the memory or even try another slot. If you have two or more sticks of RAM, try alternating them in different slots or try them one at a time. You may also want to try running MemTest on it, but that’s only if you are able to get your computer up and running long enough to complete the test.