Oh, Joy of home ownership :(

[John B.]

I have had success clearing an AC drain using a shop-vac. Slip the vac nozzle a couple inches up over the external pipe drain, wrap your hand (or some tape) across the joint, and turn the vac on for a couple minutes. You'll hear the stuff being pulled out by the vacuum (make sure you're in wet vac mode). On my shop-vac, I had to remove the hard plastic nozzle end of the hose to have enough diameter to overlap the PVC pipe drain.

My A/C company has also used an inert gas to pressurize the drain line and force the block out.