Final Analysis

Based on your input:

The computer turns on but shuts down suddenly without notice.

Conclusion:  (1 of the following Parts is broken)

This usually indicates either a failing motherboard*, power supply or fan; or it may indicate that your heatsink has come loose from the processor.  It is VERY UNLIKELY that more than 1 part would be broken; but most likely there is a broken part.

Quote for Parts, Labor, Taxes, Fees (all inclusive)

$190 - $280

*if your motherboard requires replacement, you will need to reinstall your aftermarket programs (programs installed after you purchased the computer)