Refrigerator starts -runs for two weeks, compressor won't restart

It might be but I would first check the condenser to see if it's blocked or if the condenser fan (if it has one) is not working. The "buzzing/humming/ticking" sounds you're hearing is the compressor trying to restart after it became locked down. Excessive pressures in the system or compressor overheating is usually the cause although sometimes the bearings in the compressor simply lock up.
Check to see if the fridge cycles on and off by the thermostat. If it doesn't cycle and just keeps running then the thermostat is bad and that can cause compressor failure thanks to "slugging". If it does then you want to check the defrost timer. Turn the timer's dial until it clicks into defrost and see if it comes out on its own. Check if the compressor has trouble starting after defrost. If it stays in defrost the timer is shot. If the timer times out and the compressor will not restart then the relay might be bad or, the compressor might be going bad.
A 3in1 relay/capacitor/overload might help out and give the unit a little longer time but sooner or later it will go.