Starts up then looses all power

It is almost always one of two things:

The power supply is going bad, or one of the internal fans are going bad. If the power supply goes bad there isn't enough electricity to keep the machine running. If the processor fan goes bad there is usualy a thermal protect switch that will stop the machine from starting.

Open the cover and try to turn on the machine. If all fans appear to spin I would bet the power supply. You can usualy purchase them for around $40

Power suppy. They are anywhere from 25-75 bucks.