You can view the page file usage and available RAM by pressing ctrl+alt+del, and going to the performance tab.
For page file, just note down the number by the "PF Usage" meter.
For the RAM, look to the "Physical Memory (K)" section, and note down the numbers beside "total" and "available".

Your system is fairly up to date, so if it is a resource problem, it's likely that you have a memory leak of some description, when one process will keep consuming memory, but not releasing it when finished. This is usually indicated by the computer only crashing after it has been on for a prolonged period of time, and a reboot will fix the problem.
It's very hard to isolate and fix a memory leak, so sometimes the only option is to format and reinstall Windows.

Did you install any software around the time that the crashes started happening?

Definitely do a full virus scan and spyware check, and see if that turns anything up, because memory leaks can absolutely be caused by virii.