Doom: The Boardgame?!
So, what do you do if you can't run the latest iteration of Doom? Simple. Buy a board game version. Hardware requirements are low. (Table, chairs, or possibly a floor.) Plus it's cheaper than upgrading your system probably. Plus no fancy network shenanigans for multiplayer.
Tip: If you want to replicate the Doom 3 experience fully, turn the lights off.