I had almost the exact same post a week or two ago before my sister in law and her husband came out to the house. It always seems like houseguests get the most interesting in beer since a keg is always almost empty (sediment laden), or almost full (clogged in this case).
I got no more than a few drips with every "pour" even at 25psi. I turned off the gas/disconnected it, bled all the pressure and kept the pressure relief valve pulled open so that even off gassing beer wouldn't cause any pressure build-up, removed the liquid quick-connect and carefully removed the beer-out post. This can be a mess, especially with a full keg that has any kind of carbonation, so have a few towels handy or remove the whole keg and put it into a place that can handle spilling beer (concrete floor, bath tub, a giant pitcher so you don't waste any beer, etc.).
With the liquid quick connect off, you may still not see any beer coming out the dip tube. In my case, I disassembled my beer-out quick-connect and removed the spring/pin so that it is "open." If doing this method, you also will need to remove the poppet valve from the beer-out post on the keg since the poppet needs the spring-loaded pin in the quick-connect to open. It should be noted that in doing this, while you make the beer flow easier out of the keg, the only thing stopping pressurized beer from escaping from the keg is your picnic tap or faucet in your kegerator.
Anyway, I digress. When initially removing the beer-post on the keg, if beer doesn't come out of the dip tube, remove the dip tube. Be sure to keep the pressure-relief valve open, so the beer doesn't surprise you when you get the tube out! Once you get the dip tube out, quickly take it to the sink and run something through it to dislodge the clog. Mine was so thoroughly clogged that I needed to use my wire tubing brush that is about 3' long and force it through the tube. The hops that came out looked almost identical to pellet hops since they were compressed into 1/4" round shapes, about 2' long. HA! I re-sanitized my dip tube for about 3 minutes in iodophor, and put it back into the keg. I assembled everything without the beer-out poppet and the spring-loaded pin in the quick-connect in hopes that hops material wouldn't clog things up.
There was no clog after this, and the first half dozen pours were thick with hops floaties. I'm thinking about doing it all again now that the hops have been reduced, and reassembling everything with a screen on the bottom of the dip tube in addition to the poppets and such.
It turns out that keeping all hops material out of the keg is key, unless you are hopping in a bag or something in your keg. Good luck!