Hello;
So i guess that the PSU is good. As i diagnose of what you have said, i digested a conclusion that when the computer shutdown when application run. there a problem conflicting the application to another application or such an application trigering the system to shutdown.
Some causes of this problem are:
The system is infected by known and unknown virus
The driver of the system are not properly installed
The application program committed an errors trigering the system to shutdown.
Possible solutions:
1. Scan you system with a potent anti virus
2. Remove the installed driver of the sytem and reinstall it after restarting
3. Unistall the application that causes shutdown problem and you can reinstall it after restarting.
4. remove newly installed hardware or install the correct driver of the hardware.
Note in scanning your system with antivirus you should scan it it safemode.
some usefull links:
http://www.precisesecurity.com/antivirus/online-scan.htm
If all the solution did not work to your system. please notify me for further solution.
best regards, melnavz