Just as an FYI for anyone who finds this in the future I had the same problem and fixed it by descaling (which I appreciate the original poster had already tried).
Very simple: Put a few pints of vinegar in the tank and run the brew cycle. It took about 30 seconds - started coming out slowly then, bam, started running through as usual.
Just commenting as this thread ranks pretty high in Google so others may come across it, with a similar problem, but who haven't descaled yet.