Yes, it sounds like (a little confusing) you have a ground loop problem, and yes they can matter, especially when trying to measure small analog signals. If all grounds tie back to the same outlet strip via relatively short line cords, then it would probably be OK. However, you say that this cryostat thing (whatever that is) is connected separately to building ground, so that is obviously not the case and it's confusing therefore why you brought it up.
In general, it's good to convert analog signals to digital as close as possible to the source, then ship around digital signals. Those are much easier to isolate, like via opto-couplers, pulse transformers, radio, etc. In other words, a old fashioned A/D card in the computer is not the best overall architecture from a system level point of view.
However, look at the A/D card carefully. Most likely it can be configured for single ended and differential operation. This is a case where you want differential inputs. The cryostat thingy may produce a ground referenced signal, but take its ground and output signal as being differential. This will essentially subtract the ground offset from the signal before converting it.
This trick will only work up to some frequency, probably a few kHz or low 10s of kHz. It should work pretty well in subtracting off any ground signal due to 60 Hz or 50 Hz power line return currents accross ground paths in the loop. Sharp common mode spikes can still confuse the diff amp in the A/D and show up as noise in the final output. It's worth a try though. If it's not good enough, go back and convert to digital at the sensor, then opto-isolate the digital telemetry signal.
If you use mains transformers for the audio signal it will 'work' but the audio performance will most likely be miserable. Perhaps suitable for voice. The reason is that transformers designed to pass many kHz need relatively thin and expensive laminations or the eddy currents in the laminations will attenuate the higher frequencies.
You might be better off trying to salvage something from a very old transistor radio (not the output transformer but an interstage coupling transformer). Suitable line in/out transformers are sold for auto use.. not too expensive.
Or get rid of the ground loop via a mains isolation transformer (large and not cheap).
Or design a differential to single ended amplifier to deal with the common mode voltage.
Best Answer
That approach is common in audio and industrial sensor signals for the reasons you've identified. The screen is usually left connected at the transmit end and disconnected at the receive end so that may be worth a try. Get a short male-female cable to hack and install it at the projector end.
We're short a few details on your setup. What kind of lights? Fluorescent, incandescent, dimmers, etc.
Ground loops cause problems because of either a) a difference in ground voltages between the signal source and destination or b) because of induced currents in the loop due to EM interference. Something that may be worth a try is to power the PC and projector from the same socket. This should eliminate any ground potential differences. A temporary extension lead should be good enough to give an indication. If you can run the mains cable close to the video cable it will reduce the cross-sectional area of the loop and that may help too. (I know this is usually not considered good practice and you may get some switched mode power supply interference.)