[Quoth]

There is a file that tells windows what to load based on the USB IDs. That may be wrong. That will be why a USB memory stick is OK and the Kindle is not.

You can copy the .inf files (and others) from good computer on a USB stick, and then boot to command line safe mode to copy the files to BSOD PC.

The sys files wouldn't be in inf, but a different place, such as C:\Windows\System32\Drivers as mentioned

Also, but memory is hazy, there are compiled "inf" files with a different ending that can't be looked at with a text editor. They can take precedence. I think Precompiled setup Information files end in .pnf, so copy those too.

Edit:
Possibly (do check) you can delete a .pnf file that has same name as .inf and it's recreated on first use of the .inf. Perhaps if the program that does that is faulty, the Kindle connects OK first time, then a faulty .pnf is made (somehow?) and next time you get a BSOD.

So copying .pnf files from good laptop may fix the issue but hide the cause, which may occur wan a new USB thing is connected a 2nd time.