Chances are its going to be a capacitor or contactor. Or both. The compressor sounds like it is not starting because of a failed contactor or capacitor on the compressor side. The fan side start still works but is not getting a run signal from the compressor and it shuts down. Compressor attempts another start cycle all over again, but fails over and over.
If you have a warranty, pay the service charge and have them repair it if covered. If you misdiagnose it, and do an improper repair, it will cost way more than the $95 service fee. You ARE a certified and licensed HVAC repairman aren't you?