It spins freely by hand. But when plugged in, yes musical chord. Is there a capacitor or something I can replace?
Some earlier versions of the water circulation motor had three-wires & one went to a run capacitor down next to the compressor area, these were a permanent "split-phase" type motors, yours doesn't sound like it is (or was) since your re-soldered it with only two electrical leads/wires, sounds like the prior post has a solution for you provided you can adapt your impeller to the shaft, Funtronics or Sodajerkwerks may have a replacement impeller that would work.
If you had an ohm meter you'd be able to measure the resistance across the wiring leads & see if it's an open winding.