Reddit mentions of OEM Upgraded Trane American Standard 1/6 HP 230v Condenser Fan Motor MOT10478

That helps. First, it would be remiss of me not to tell you to be really, really careful with those capacitors. You've already replaced one so you're confident and competent enough to break into your appliances so that's good, but that big bastard can kill you. I don't mean to sound condescending or hyperbolic, but caps are nasty devices. I toy around with tube amps and I've been zapped by some of the smaller ones and it THAT hurt. I can't even imagine what one of these things would do, if it didn't kill you that is. Just double triple check that the breaker is off whenever you tear into this thing in addition to taking caution around the caps.

End disclaimer.

When you replaced the cap, did it have all the same characteristics and did you make absolutely sure you put all the wires on the proper terminals? The two main specs to look at will be voltage and capacitance but tolerance and environmental requirements should be similar. If everything you've already done is in order, it sounds like you probably just need a new motor which unfortunately looks to be kinda pricey for that model. The internet tells me the motor model is MOT10478 but you might be able to find a more generic part if you dig around a bit. Either way, $2xx is far cheaper than a new condenser or the cost of a motor plus professional installation.

I'd like to tell you a better way to make doubly sure your motor is actually the problem, but I can't think of a way to do so safely. It sounds like it's the motor, but I'm damn sure not going to be responsible for telling you to spend $250+ to ultimately get nothing. To get at it you'll have to remove the hex bolts along the outside top edge of the condenser shroud so you can pull the top off and get at the motor. I WILL say that there might be a chance that there's a problem with the controller or the voltage going to the fan. You could probably hook a volt meter up to the input leads of the fan (the ones that go from the starter cap to the fan) and make sure it's getting 240 but again, if you're not comfortable around a digital multi meter or aren't familiar with electrical safety I'd advise you not to try it while the machine is on. Best of luck.

Edit: This is a pretty legit walk through for motor replacement. If you do go through with it, make sure the wires are all tucked away before you test. No sense in slicing your fresh work.

http://www.instructables.com/id/Change-Ac-Condenser-Fan-Motor/