the dual starting caps are essentially 2 capacitors in a single can with separate wiring terminals on top. so, one can work and the other not work.
the starter cap will be much much larger for the compressor than for the fan motor. for example, the one on my house 3 ton unit is a 60/5 MFD. 60MFD for the compressor and 5 MFD for the fan motor.
it gives the extra umph as the motors age to get them started.
there is also a kickstart capacitor that adds even more that are available.
http://www.kickstartoem.com/products/products.html
i still would be checking voltages to be sure they are ok. hopefully you didnt burn out the motor.