I think it's a problem with your motherboard or PSU. Low-end PSUs usually fail at stabilising voltages. Motherboard capacitors get killed after few years and PC starts to behave strangely. Starting problems are common, sometimes hardware fails mid-work as you've described.
I'm afraid it's too late now. I guess your PSU is dead, very likely motherboard will need replacement too. Hard drives may be damaged. It's possible that repair won't be worthwile.