Well, here's what I'd try. It's only temporary, it's less than ideal, I haven't tried it, etc...

An AC gets cold on one side, hot on the other. The cold side needs to be in the room to be cooled. The hot side just needs to be outside the room, not necessarily outside the house. I think I'd try setting the AC in the door (on a table or stool) and build a cardboard "door" around the AC unit (you could just cut an AC-sized hole in the door, but that's messy and kinda permanent). The heat the AC removes from the computer room would then be dumped into the rest of the house. If you open the windows, it's practically outside. :-) Put a bucket under the AC to catch the condensation.

Yeah, it's a hack. OTOH, "Brute force has an elegance all its own."

Note that just setting the AC in the door without blocking the rest of the room entrance won't work. The hot and cold air will mix. Instead of cardboard, you could use blankets, tarp, plastic, etc.