Which W-7 Memory Diagnostic tests more than the first 4GBs of memory?

My HP 8300 System has 16GBs.
I have run several tools with no errors reported.
I did read where the W-7 tool only checks the first 4GBs.
Is there one that will test all the memory installed?
Thank you in advance for your feedback.

I was having so many recoverable blue screens that I decided to swap physical PC's.
I have had another identical used PC that I haven't used in about five years.
It was physically banged up when I purchased it on the Internet.
At the time I ordered two so I would have a spare for parts.
I have been using the one that wasn't physically banged up since then.
I just swapped the hard drive from the pretty one to the banged up one.
I had reasoned that if it were a memory problem, it would stay with the pretty one.
The banged up one booted right up and appears to be running just fine.
My concern is, Windows wants to re-run the Experience Level as it senses new hardware.
I am afraid that when I do so, it will cause Microsoft to say the Software is not valid.

Does anyone know what will happen if I run the reassessment?

One thing you can do is remove one stick at a time and run windows to see if you get a bsod. More information on your blue screen is needed however. Blue Screen of Death (BSOD) Posting Instructions Memtest is one of the best programs for testing memory. MemTest86 - Official Site of the x86 and ARM Memory Testing Tool You will have to burn it to a cd or create a bootable usb because it doesn't run in Windows. You will have to run it multiple interactions for an accurate test. I read that it needs to be run 8 times. Perhaps someone here can confirm.
How to Test RAM: Making Sure Bad Memory Isn't Crashing Your PC | Tom's Hardware
How To Test Memory Using MemTest86 - Overclockers Club
memtest86+ - How many passes are enough with Memtest? - Super User

As for the reassessment I'm not sure exactly what it will do but I think that Windows is going to be deactivated and require reactivation since it was placed in a "new" computer.

Sorry but I can't, except possibly on a 32-bit OS which only supports 4 gb anyway (without special modifications).