"If my memory is bad, wouldn't it create a BSOD in safe mode as well? Why can I get around in safe mode with no hitches, but normal mode dies after a few seconds. "
If you haven't ran any tests on the memory you are kind of guessing that the memory is the issue.
When you start in safe mode a bare minimum of drivers are loaded.
The computer is using skimpy generic drivers & just enough of Windows/programs to make the computer work.
That would mean that much less of the memory is being used .
There is the possibility that in safe mode there isn't enough running so what you're doing in safe mode never tries to access the faulty part of the memory.
If you want to know for sure if your memory is the issue download Memtest86,http://www.memtest86.com/memtest86-3.5.iso.zip
Unzip the iso file & use a burning program [like Nero] that has the "Burn image to disk" feature to make the disk.
Put the disk in the drive, start the computer & let it boot & run the test.
If any errors are found the memory is bad.
You have to exit the test or eject the disk & restart the computer to stop the test .
Memtest89 will keep running unless you stop it manually.
It is also available to make a floppy disk if you prefer that,http://www.memtest86.com/memtest35.zip
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