Check one of the major memory manufacturer's website for their "memory configurator" to pick the amount of RAM your system can handle (Corsair, GSkill, Kingston, etc)
If unable to figure it out, contact them for assistance. You'll get a sales person, but they'll help to tell you what you can do (then you can say "thank you" and buy from whomever you please).
Hangs can be caused by outdated nVidia software.
I'd suggest visiting the nVidia website to get updated drivers for your video and nForce chipset (it's found under the Legacy devices now).
On this page: http://www.nvidia.com/Download/index.aspx?lang=en-us
Select Legacy, then select nForce 4 Series, then select nForce 430 / GEForce 6150 SE, then select Windows Vista 64 bit (there is no option for Windows 7)
You may have to run the installer in compatibility mode for Vista - but try just double clicking on it first.
Due to the age of this system, I have to ask if you won't be better off by purchasing a new system?
I'll continue to work with you on this - but it might be time for a new system for you, and that would save you a lot of work
The memory usage I cited was from the systeminfo.txt report.
This is a one time reading of the memory, so it could be at a point where the Desktop Weather app was hogging RAM.
The point here is that excessive RAM consumption can lead to problems - including BSOD's.
I'd suggest temporarily uninstalling the Desktop Weather app to see if that helps.
No need to mess with the HP Recovery drive. Leave it alone so you can use it if it's needed.
For the hardware diagnostics, the easiest thing to do is to run the Seagate Seatools diagnostics (long/extended test).
If unable to run the bootable test, run the Windows version of the test.
Verifier instructions were designed to be terrifying - but they work well as I've listed them.
As long as you do the first 4 steps, you can recover from any problem with Driver Verifier.
But, if you're not feeling up to it, we can wait on it until later.
Finally, please see my PM