Sudden shutdowns are almost always due to overheating. Especially if it happens a consistent amount of time after turning on the computer. Get a can of compressed air, take the laptop outside, and blast the air into all the vents. Blast it carefully into the fan vent (don't let the fan spin up too fast). If you see huge dust plumes billow out of the laptop, keep blasting until no more dust comes out. Then take it back in and try running it again. it should work. The dust was blocking airflow, causing the laptop to overheat.
If you don't hear the fan spin up from the compressed air, turn on the laptop and put your hand over the fan vent. See if you can feel air coming out. If no air is coming out, either the fan is dead and needs to be replaced, or it's so choked with dust that it can't spin. You'll have to open up the laptop and try to clean the fan manually, or replace it.
Install some sort of hardware monitoring program like hwinfo and look at your CPU temps. If they're still high (roughly 80+ C for a laptop, though it varies with processor), depending on how old the laptop is you may also need to reapply thermal paste between the CPU and heatsink.