Computer trips GFCI
 

Lately the computer has been tripping the GFCI in the wall (US, 120 volts). It happens when I am not in the room so I don't know if it has any warning signs. It is running fine right now, but when I get up in the morning I will probably find it dead. I have it plugged into a regular outlet to test it and it has shut itself down once today.
When I start it the beeps are not normal. The first single beep is as expected, then it seems to give a series of random, rather quiet beeps that make no sense.
I don't know if it is safe to leave on not plugged into the GFCI but it may be that the GFCI itself is faulty so I will change it out and try again, but has anyone had this problem and what did you find?

change the PSU in the computer before it blows completely and causes a fire

The concept of leaving a known faulty piece of equipment running all night unattended is mind blowingly silly and as Milo says potentially dangerous.