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Check the door seal first - a leaky gasket makes the compressor work nonstop because the fridge can't hold temperature. If the seal looks fine, feel the coils at the back; if they're caked with dust, clean them out since that blocks heat transfer and forces the compressor to run longer. A compressor that cycles on and off normally is healthy, but constant running usually means either a seal problem, dirty coils, or the compressor itself is failing - the first two are easy fixes, so start there before assuming it's dead.
If the compressor's been running for hours without cycling off, something's definitely wrong. The fridge should kick in and out throughout the day - a constantly running motor means it's fighting to reach temperature and losing that battle.
Most common culprit is airflow. Dust buildup on the condenser coils (usually at the back or underneath) chokes the system and forces the compressor to work overtime. Unplug it, pull the fridge out, and vacuum those coils hard - you'd be surprised how much junk accumulates back there. While you're at it, make sure nothing's blocking the vents inside the fridge itself. A frozen-up evaporator (ice blocking airflow from the freezer section) does the same thing.
If the coils are clean and vents are clear, the thermostat might be busted and not telling the compressor when to stop. That's trickier to diagnose without a multimeter, but it's worth knowing it's not always a mechanical failure - sometimes it's just a faulty sensor. Temperature should stabilize between 35 - 38°F in the main section; if it's creeping higher or won't hold steady, the thermostat's likely the culprit.
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