|Almost all linux cd's offer memtest. It is a very basic test that has little to do with real world faults unless directly related to memory.|
There are other commercial diag suites.
A simple test is to run live cd's/usb's and see if fails also. You can make a windows live cd too..
See event logs if it boots.
Might have to diag power supply.
Set bios settings to default or fail safe to begin with.
"Best Practices", Event viewer, host file, perfmon, antivirus, anti-spyware, Live CD's, backups, are in my top 10