Sounds very much like a power supply problem. Does it have a separate power adapter, or does the mains lead plug directly into it? If you can somehow get your hands on a replacement power adapter that would be well worth trying. If not an exact replacement it will need to have the same size plug on the computer end, the same output voltage, and the same or greaterAmps (or Watts).
Otherwise, I'd take the back off and see if you can spot any domed electrolytic capacitors in the vicinity of where the power comes in. (See https://therestartproject.org/wiki/Basic_electronic_components#Fault-finding_and_Repair_3)