My go-to dmm has a cap checker on it. It's a "lowly" fluke 12. It doesn't read current, though. I have learnt my lesson in that regard: if I really need to measure amps on something, a non-contact clamp won't blow a fuse in my meter. I have had more meters than I would like to count, but this one refuses to get lost or stolen, and has survived everything I have done to it. I really appreciate a good tool (sniff)...
That compressor really could have had more oil in the sump. Do you think you can weld it back together?