I have the 1998 version of Baldur's Gate (Forgotten Realms).
I was playing the game, chapter 4, Cloakwood Mines (level 2 of Mine). I clicked on one of the doors in the prison area, and it suddenly glitched out and brought me to my computer's bright blue system reboot screen. I turned my computer off and tried to play the game again later.
Now when I click "single player" then "load" it glitches and closes the game, saying...
"An Assertion fail in D:/Baldur/InfScreenLoad.cpp at line number 1344"

I sent this into the site and asked for help but if anyone else has any ideas, please tell me. I would like to finish the game!

Ouch, Blue Screen of Death how we loath thee!

You may want to wait for more suggestions before trying this but:

Does it crash before or after you choose which savegame to load? If after, try a different save.

If it crashes before it even brings up the savegame list you could try this: Go into your Baldur's Gate directory and find the savegame folder, it should be named something like "saves" or "savegames" something along those lines. Copy and paste that folder anywhere outside of the baldur's gate directory. Uninstall Baldur's Gate and then Reinstall it. Then copy and paste the savegames you took out previously back into the Baldur's Gate folder where they were originally.

Hopefully that would remedy your problem. Also, make sure you are patched up to the current official Baldur's Gate patch. (if not, try that before attempting the uninstall/reinstall)

I tried the reinstall, but the problem is the same.
I'm not sure how to update the game. How does that work?

If the reinstall didn't work I have no clue what to tell you except keep your savegames and try from a different computer when you have the opportunity.

It looks like BioWare still supports baldu'rs gate (they developed it, gamesas published it)

http://www.bioware.com/games/baldurs_gate/support/patches/

That's the link to the patches, looks like they also have a support forum. You could try emaling too.