According to Tony Berlin :
Not true. A single adjacent shorted out winding will cause the current draw to go way up, but the motor will usually still turn fine (more or less).
I think Turtle may be drawing attention away from the right thing to check, but he's quite right insofar as motors can easily draw more than they should. Ie: shorted windings, stiff bearings or seals, etc.
The fact that the condenser wiring is melting is very suggestive (especially after wiring and condensor replacement), not of a winding or condensor problem (a shorted condensor could do this), but that of the start switch.
_Normally_, the condenser is only connected to the start winding for a few seconds at most while the motor is getting up to speed. Once the motor nears operating speed, the condensor and start winding are switched off. The condensor wiring shouldn't be in-circuit long enough to get hot even if it is drawing too much current.
Having the condensor wiring overheat is suggestive of one of two things:
1) the start switch is malfunctioning and holding the start winding in-circuit too long, and (possibly in addition), there's a short in the start winding and it's pulling too much current when it is in-circuit. 2) The motor is taking WAY too much time to get up to speed (bad bearings, semi-seized seals etc), and hence the condensor circuit is remaining in-circuit MUCH too long.There are other possibilities (ie: the condensor capacitive value is _grossly_ wrong, but unless you have gremlins running around replacing start condensers without you knowing it ;-), unlikely)
Motor windings rarely fail and are quite expensive to "repair", so I'd concentrate elsewhere first.
I'd look into the start switch and making sure it's not fused (spot welded) closed. Often just "unsticking it" and polishing it up with a nail file or similar does the trick.
Also check to see whether there's too much rotation resistance. Maybe it needs new seals. Or a new compressor. Ugh.