Quoted from Tickerguy:

Getting those caps off is not hard. Use a temperature-controlled solder station, set it HOT (~700F) and have your solder sucker ready. Flow it, hit it, done. Do the same on the other pin and it should drop out.
I pull parts like that all the time; the secret is to make it happen FAST before heat can transfer to things you don't want it to and damage components (like lifting traces or via's!)
But that cap doesn't appear to be bad. Got a cap checker? Don't assume, test! No ESR problem and capacitance is in-spec, leave it alone.
3 coils not working and the rest are ok? Odds are it's not the cap. Check the wiring to the coil and the driver transistors; are you seeing voltage on the output of the transistor *and* trigger on the drivers? My money is on the problem being there instead of at that cap.