Looks like you could also be experiencing hardware failure from a system of this age. This system is about 8-9 years old. What I usually do with a system like that comes in to be repaired is to test the hardware first, before attempting software solutions. That's cause I'm a hardware engineer. The software solutions suggested will only work if the hardware is ok. I would suggest that you test the hardware, and I'll give you a couple of links to do so. Once that's done, you should consider getting a new hard drive and removing the old drive, and put the new drive into the PC and install Vista from factory Recovery Media (most likely they will be discs). This will reinstall the Vista that originally came with your computer from the factory when it was new. If the BSODs stop, then it was due to your having a faulty hard drive. Failed hard drives in systems the age of your PC are the #1 cause of failure.
Having set aside your old hard drive, you can use data recovery programs to get your stuff off of it, in the case you don't already have it backed up to external media. If you don't know how to do this, you can take that drive to your local computer repair shop and pay a professional Tech to recovery all your library files (Documents, Photos, Music, Videos, Movies, E-mail, etc.). Here are the links to the hardware diagnostics I mentioned to test your PC: MEMORY DIAGNOSTICS
: Memory Diagnostics HARD DRIVE DIAGNOSTICS:
Hard Drive Diagnostic Procedure
Starting in 2007, when Vista computers came first came out, very few of them were provided with factory Recovery Discs. However, some were and if you have those you can reinstall Vista onto a new hard drive. If you don't have those discs or lost them, you can still buy them direct from HP for $29-$99 U.S.
After testing your RAM sticks, installing a new hard drive, and a clean install of Windows Vista, and your BSODs continue, your Motherboard is bricked.
That normally is a $275-$500 repair cost, and doesn't make sense to fix, given that brand new PCs cost less than $225.
One thing that wasn't mentioned was whether you were using a plug-in Graphics Card or the internal Intel GMA 3100 Dynamic Video Memory Technology 4.0 Graphics chip built into your HP Motherboard. Should you do this testing and Vista reinstall, make sure to remove the plug-in graphics card and use the embedded Graphics Chip to test the computer
. If the BSODs continue as above, your Motherboard is toast and it's time to replace it or replace the entire computer which will probably be cheaper. There is also the issue, that you may no longer be able to buy the replacement Motherboard online such as on ebay, as due to it's age it may not be available in the aftermarket.
Good luck! <<<BIGBEARJEDI>>>