I am very glad that this worked for many of you or at least pointed you in the right direction.
Just felt that I'd mention that if you download and install that "Restoration Project" from No Mutants Allowed - Your Post Nuclear News Center!
that it fixes the problem as well.
After you do a clean install of Fallout 2 V 1.02d and install the Restoration Project to the install directory, you can start the game and go into the "Options" button on the main screen after the intro videos. From there, at the top, there should be a new button I believe called "sFall" and you can play with your resolution and bit depth options in there! Been using in on a brand new computer and works fine.
Of course, you can just still with the tried and true Task Manager to open or close explorer.exe!