I replaced the capacitor on my Lennox ac unit today. If you have a bad cap (or at least the compressor portion of a dual run cap), the compressor won't kick on. If you have a multimeter that can read microfarads, you can test the capacitor yourself and possibly save the service call. Turn off the power, disconnect the wires, discharge the cap using a screwdriver from common to fan and common to herm (compressor). Pull cap (makes it easier) and test the common to herm with the multimeter. The cap should say on the side what the normal reading is and what the tolerance is. If it is out of tolerance, replace the cap.
http://www.hvacpartsoutlet.com/troubleshootacapacitor.aspx
I am not an HVAC tech, so any pros feel free to comment on what I posted.