Re: AC compressor starting/stopping
Yes, the original contractor should by all means return and address the problem, and sooner rather than later! I am not completely sure if you are referring to the compressor or the condenser (which would be a completely new outdoor unit, while the compressor is the major component inside an existing unit).
The short-cycling could be any number of things. If you can't get someone back out there in a reasonable amount of time. (Simply because your unit is 'running' is not a reason to put you off. You can tell them you have no cooling, as you don't). But, if you don't get any results, call the manufacturer and let them know. They may be able to recommend a competent contractor to look at it.
All the best, Irishmist
Live your life as an EXCLAMATION; not an explanation!