Yes, you'll want the following tested:
1. Run capacitor capacitance
2. Compressor windings ohmed out, resistance
3. Wires leading to the compressor
4. Airflow and condition of the indoor coil - plugged coil can kill compressor, i think
5. Metering device - a failed txv can kill a compressor, plugged orifice
6. Contactor closed resistance, voltage at the outdoor unit
If something external killed this compressor, the next one will fail too. Isn't it true that compressors rarely die early, they're killed or murdered by something else?
If this compressor is mechanically stuck and everything electrical checks out, request that a hard start kit be put on it.
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11 years isn't old for a coil; think they're supposed to last 15-25+.
If r22, i would consider springing for a cheap r22 dry unit (goodman or icp may do fine) which can also run on 407c (compressor has to have peo oil in it) to mate to the old coil - should be okay if both are 13 seer.