Pull out the dip tube again and clean it out, re-sanitize and try again. Repeat until it's clear.
You could try transferring the beer but I'd try this first. Last time this happened to me I think it took four or five iterations to get things flowing smoothly again.
Well...this sort of worked. After 6 or 7 iterations I got the keg to flow good. Put it back in the kegerator...which swirled up more mess and it plugged again. I repeated the cleaning of the dip tube and post a few more times. Including moving the keg around to get stuff swirled up. Got it going good again, put the keg back in the kegerator. And it plugged again.
I'm taking a break to watch football and drink beer. I'll try it again later.
Denny - wouldnt the sure screen cause CO2 to come out of solution as the liquid pass through it?