Sounds like a faulty contact somewhere, probably on the RAM sticks. Get yourself a bottle of isopropyl/rubbing alcohol and disassemble your PC. Meticulously clean every single component and its contacts with the alcohol. Take extra care with the copper contacts of the RAM sticks and the GPU. Try using
this method. Clean the power cables coming from the PSU as well, just to be sure. Clean the dust out of the DIMM slots and PCIE slots etc using compressed air or a vaccum cleaner.
Imho, that should fix it. How many RAM sticks do you have? You said the customer service guy replaced one of them, but have you tried using just one stick?
Also, when you did randomly get the PC to run, did it ever crash? Did you try stress testing it with a game or a tool like OCCT? Next time do a stress test and use HWINFO to verify that all the temps are reasonable.