Compressor problem?

Question

My outdoor unit comes on with the fan blowing just fine. Then I hear a buzzing sound for about 2-3 seconds which I believe is the compressor trying to come on. (Incidentally, a couple of lights inside the house seem to dim at the same time that the buzzing sound occurs.)The buzzing sound reoccurs every couple minutes while the outdoor unit fan and the indoor blower both continue to run. I have shut down both the outdoor and indoor units for a couple hours and tried restarting but to no avail. I took the cover off the back part of the outside unit where the compressor sits and it was disgusting inside. I cleaned it out, but it is by no means spotless.Is my compressor shot?