Charge it up.....place your tongue across the leads.
If you can still speak, it needs replacing.

<edit>..My smart-ass replies aside, I spent a few years fixing slush freezers, and the compresor setup is about the same as a fridge.
From what you are describing, I would swap out the capacitor with a known good one...and just for test purposes, just about any similr-sized cap can be used (hit your local used appliance shop and they will have a million laying around, or even borrow one off your chest freezer for testing).
Also check your start relay, a bad one can work "sometimes"...and to rule out the thermal overload, just remove it from the circuit.
But from the description, I would say the 2 most likely culprits are the cap, or the compressor itself.
[This message has been edited by MidEngineManiac (edited 06-17-2010).]