1994 Buick Roadmaster.
Went to start and the battery was run down. Hooked up charger and I am hearing an electric motor/fan running under the air cleaner housing.
What would be under there and why would it be stuck on?

This is a neighbor'* car and I am tending to it for the summer while he is up north. Would like to get it sorted out before he gets home.

That sounds like the general area where the air pump would be for the ELC (Electronic Level Control). It essentially pumps air in to the rear shocks to level the rear of the car with a load. I would trace air lines, and rear shocks, unless the rear of the car is elevated already and the pump continues to run, in which case I would check the sensor on the rear suspension.

Thanks, Randall,
I pulled fuse and relay for air pump and have battery on charger and pump is not running.
I am assuming there are metal/rubber lines running to the shocks and suspecting maybe rust and deterioration, but will try to check everything out once the battery is up.
Two years ago he had to replace rusted ATF lines between transmission and radiator. Vehicle is from Wisconsin (road salt) and had not been run for awhile before he got it from his mothers estate.
I have been starting the vehicle about every three weeks. About six weeks ago after I turned the car off I heard a motor running when I got out. It shut off shortly so I didn't think too much of it. Last time I heard it running and assumed it would shut off so I left. Wrong!! Came back to find totally dead battery.
--Ard

The rubber bag part of the rear shocks or struts can deteriorate also, and that can cause the pump to continue to stay on, if not that it could be a line, but check the shocks first, if you can get a picture of the rubber part on them, and post it.
If it is neither of those, then as Randall said, it could be the level arm sensor on the rear of the suspension.

If the pump ever totally fails/dies, I'd consider getting shock replacements, they have some with a conversion kit that allows you to manually raise, or lower the rear suspension.
Of course if it is possible, and cost effective, then try to replace whatever you need to so you retain the factor air leveling system, I had a similar problem, and replaced my rear struts, and the problem was solved.