Hi rose2948...there are many things that cause overheating and it's something which can affect machines which are only on for a short amount of time (hence why some shutdown on their own). You mentioned that the inside of the machine was heavily clogged up with dust and this alone is a major cause of overheating. Regardless that the machine has since been cleaned, the fans could be permanently damaged, thus not cooling/extracting air from the unit in the correct manner. Also, if some hardware is faulty, that can cause overheating too.
At this stage, i'd advise asking your friend to check that the RAM and graphics card are seated correctly. If they both are, the next step would be checking the integrity of your RAM which can be done using a utility called memtest86 which can be downloaded
[here]. Please note that this test can take a couple of hours to complete. If you have multiple modules of RAM, it would be best to test them one at a time and if any errors are found, that would be the problem.
Also, knowing the exact number of beeps may help find out what is wrong as the number is specific to the fault....but they also differ depending on motherboard/BIOS versions so that would be handy too please.
Hope that helps :smile: