As far as I know, those results (if correctly done) pretty much exclude everything except bad memory, some program (or driver) that is totally locking up the computer, or the CPU overheating.
All though CPU temperature is the least likely, it is also the easiest to check. I use Core Temp
. If you click the "More downloads..." link and select the standalone version, you won't have to use the silly InstalllQ downloader. With 30 seconds, I don't know how much time you have to get it working and reading, though! Try holding the [Shift] key down immediately after logging on until the desktop is ready to use and see if that buys you extra time. You can also try opening Task Manager (press [Ctrl]+[Shift]+[Esc]) and terminating Explorer as quickly as possible after logging in, and then starting it again by clicking "File\New Task (Run...)", typing "explorer" and pressing [Enter]. This should cause all the auto-launch programs not to load, which will reduce the CPU and memory load, possibly allowing the computer to work longer.
You can test for most driver problems by booting into Safe Mode. To test for a program that might be causing the problem, go to the System Configuration Utility (press [Win]+[R], type "msconfig", and press [Enter]). Select "Selective startup" and de-check "Load startup items" and reboot your computer. Note that HDD failure can cause any certain program to freeze the computer if that program tries to access a file that is located on a sector that is now bad; so let's keep that in mind as well.