Use a source port, you may have better luck:
http://www.doomworld.com/classicdoom/ports/

G.

Read the README.TXT file. Basically, no sound or joystick device will work
with DOOM2 unless the assigned IRQs  are in the range 0-7. And getting a
modern PC with plug-and-play to manually assign one of these IRQs rather
than auto-assign can be hard work.

What you need to do is whatever is necessary to make yoru game pad behave
the same way as the game pads that DOOM2 does know about.

But as some one else said, a DOOM2 port might be easier to work with.

S