If you can get Doom to work, Doom 2 should also run fine, as it is mostly the same game with new level data.
Doom II may be purchased through Steam. It is preconfigued to launch through DOSBox, but the file doom2.wad may be copied and used to run a source port instead.
Doom is open source, and there are many modern Windows ports of it available. This approach may be preferable to emulating the DOS version. To make any of the ports work, you will need to copy the file doom2.wad from an installation of Doom II to the directory of the source port. Some source ports include:
- ZDoom - the fastest running doom port but the graphics look pixelated.
- GZDoom - a coppy of ZDoom but graphics look better. Uses OpenGL.
- Doomsday - the prettiest port, but buggier than ZDoom.
- Chocolate Doom - replicates DOS Doom behavior as closely as possible