I t will satrt up an run but computer keep shuiting down

It could be a couple of things 1. the computer Cpu fan is not working or is clogged inspect it and clean or replace.2 The power supply could be bad

Your system is likely experiencing thermal shutdown. This could be happening at either the CPU or PSU. (In most cases.)

1.) Check your CPU fan. Is it clogged with dust because you haven't maintained it? Have the bearings died? (Is it grinding?) Replace the fan if necessary (they're cheap enough...) AND clean all of the dust from your system.

2.) Check the thermal transfer material between your CPU and CPU heatsink. Is it old and dried up? Did it ever actually make contact with the surface of the CPU to begin with? If it hasn't been replaced in a long time anyway, clean it off of the CPU and the heatsink and replace it with fresh thermal paste. (Don't use too much. Most people do. Just enough to give a thin covering!)

3.) Is your PSU full of dust to the point where it can't breathe? BLOW IT OUT! Use an air compressor if you have one. (The best way.) If not, use a basic can of air from the office supply store. (Less effective but still works.)

Beyond this... You might be having CPU/memory errors. Depending on the OS you're running, it might be causing kernel panics or other similar errors and shutting the system down. If the system is just locking up, the watchdog timer (a common function in motherboards) might be active and cycling the system. Check error logs and or SEL logs in your BIOS.