How do I clean an AC condensate pan?
I had the same issue recently on my HVAC as well.

You probably have a PVC pipe running from the bottom of the evaporator coil housing. The blockage is probably in there somewhere. You can disconnect the PVC and let the condensate drain into a bucket. 

If it does drain cleanly into a bucket, your blockage is in that drain line. Either snake it out or replace it. For me, snaking a 3/4 inch PVC with several 90-degree bends was more difficult than buying a couple pieces and replacing the drain line with 45-degree bends that are less prone to becoming blocked.

I filtered the condensate where my new drain discharges into my sump with a paper towel and was shocked how much debris was being flushed out.