How can you tell if a fuel injector is dead or just needs desperate cleaning?

test injector harness for power to suspect injector, and check for flashing ground to injector when running , if all is good , you need to test for injector resistance ( ohms) to see if it is in specs. If all that looks good , you might need to run a strong cleaner through the injectors, esp if it has high mileage. Try using a high grade fuel with alcohol , as it has good cleaning qualities .

If your injector is dead your car wil have a permanent mis and will only run on 5 cylinders where if its dirty it would only miss from time to time.Just replace al 6 their not that expensive