SC,
I just had my pump apart on my 1604, and it worked well. I flipped the tubes around so there's now fresh tubing in the pump. The hardest thing is just remembering how everything goes back together. You may want to snap some pictures as you take it apart.
Have you tried filling your capping station with flush from a flushing cartridge, and then do a cleaning? It does a great job of cleaning the tubes. But you may have a pin hole in the tube that is blocked, and that would be the reason that it blocked. If you flip the tubes as I did (if you have a pin hole), it'll be on the other side of the pump, so it won't cause a problem.