I used the win 7 memory tester, it said everything tested OK but it only took about 15 minutes to run, I don’t think it did a very extensive test.
The computer is just randomly stopping, I had something like this happen on a system about 10 years ago, it turned out to be bad ram.
That makes it a little different. Have you tried reseating the memory?
Also make sure that it's not an overheat problem, especially if you have pets. Pet hair loads up fans and causes an overheat trip with no warning. Make sure fans are not blocked and heatsinks are clean. (some laptops have 2 fans)./johnny
Could be your cooling fan. It could be stopped, or just dirty.
Was that computer made between 4 years ago and 1 year ago? Does it have an Nvidia graphics chip in it? If so, that is your likely issue.
That could be anything, including overheated CPU.
“The computer is just randomly stopping”
If it is happening on reboots from updates when you’re not there, it could also be the display drivers, or the V-RAM.
The display not re-syncing on Windows startup is way more likely than the main RAM failing.