My computer is randomly shutting down. Sometimes it will work and other times it will not. I think the processor is overheating and causing it to unexpectedly shut down. the screen goes black, the power light goes out, and all of the computer's functions stop.

Few reason for the shut down
Could be heat, electrical,

1. try cleaning all vents with compress air in order to remore dust and fuzz that can be cloging the vents.
Once this done, verify that fans works proprelly,(check air flow coming out of vents) if they dont they will need to be replace or cleaned out.

2. Check power supply unit, and battery.
Sometime power supply unit is defective, getting too hot and power output is not stable and shuts down the laptop. ( change power supply unit) check if battery hold charge. if not change battery

3. Check connections for looseness and contact

If all seems normal,and none of the mentionned point seem to be defective, the cause is deeper and would need to be looked at by a technician.