Q: I have a whining squealing noise coming from somewhere in my pulley system and serpentine belt.

I recently bought this car and had problems getting it started and there was a squeal or whine under the hood that coincided with acceleration. Upon inspection I found the battery was busted and was therefore replaced. I suspected that the alternator was overworking itself to make up for the busted battery. Cranked up immediately now but the squeal was still there but sounded somehow different. I checked power steering fluid even though the steering wheel moves freely. The fluid was low but not empty, and filled up to the c on gauge. No change in noise so I remove serpentine belt to manually spin each pulley. I started on tensioner and idler pulley because I have heard their springs and bearing tend to go bad around this mileage but spins freely. A/c, alternator, and water pump pulley spring freely with no noise also but the power steering pulley had slight play and made a single click. Is that normal? Also when running the tensioner pulley sometimes moves slightly up and down.

My car has 155000 miles.
My car has an automatic transmission.