You could rewind the transformer if you wanted but it'd probably be easier to just to yank a working one out of a similar device, they generally speaking are 12 volt transformers though you need to determine the voltage before you do anything. Difficulty is pretty much across the board depending on what if any potting compound was used for the windings (some of them are downright messy) To properly copy the old transformer you have to determine the wire gauge of the primary and secondary, and the number of turns in each. What you're really trying to do is match the DC resistance, total number of turns and turns ratio as closely as possible. If your transformer is toast though that might be a problem as you're not going to be able to determine all of those. I'd match it with a transformer that's roughly the same size rated at 12 volts and see what happens.