This seems to be a common occurrence: Computer refuses to start, and often makes beeping noise.
I open up the case, see that the CPU heatsink seems to direct a lot of air towards the RAM (and there is usual a buildup of dust on the RAM). So I pull out the RAM, wipe the RAM terminals, plug it into a different socket, and the problem is fixed!
Its amazing how dust can wedge its way into memory connectors and (presumably) cause a connection problem.
Then again, I’ve also seen similar symptoms when a power supply is about to fail: computer will either refuse to start (and may or may not beep), or will suddenly shut down, or suddenly restart (or only restart after a ‘rest’).
And in similar circumstances (computer will suddenly shutdown a minute or two after startup, and won’t restart unless it gets a ‘rest’): cause can be an overheating CPU (either the heatsink compound has dried up, or the heatsink is not making contact with the CPU).
Its just a process of elimination, until the fault is found.