1993 and I think it was a beta.
Went up to the Exchange (same one where I saw Wolf3d when it came out for the first time).
Saw one of the guys who maintains the display computer at the Exchange and asked him about it and he let me play. IIRC he tried to setup nullmodem but it wouldn't work. I figured out how to get out of whatever shell they were using to demo the computers (think it was running on top of Windows 3.1).
I also put Doom in an ALT+255 directory and/or renamed the files to ordinary looking files so it couldn't be found in case someone else found the game. Occasionally I would go up there and play Doom.
I remember one time playing a Barney mod on Doom up there and a little girl crying when she saw it. Ah, good times.
As far as specs it was probably a 486SX or DX. Can't remember.