"Garbled and warbly" may mean the cart is disfunctional as you say. Some damage will show up on visual inspection, if you have a clear recollection of how the cart looked when new. Inspect the cantilever to see if it is centred in the mount. Other damage--a failed suspension for example--may be invisible and not show up until you try to play a record.
Is it possible the VTF is reading wrong? That might happen if the counterweight has moved. A setting much too low or much too high might give you garbled and warbly (although warbly might be TT speed instability too, I suppose).
You could start over again, as Ncarv suggests, right back to remounting the cart and balancing the arm. Check to make sure the stylus is clean, first!
It's just a thought, but if you moved the TT to the shelf with the main platter still mounted on the bearing, the suspension could have bounced some. A lot of bounce can throw settings off or worse.
