Hi Beano
What is happening to your hen sounds almost like a carbon copy of what happened to one of mine back in August. Ours had already stopped laying (she is about 2 1/2 and a hybrid).
The first thing she would do in the morning is drink loads of water, she refused pellets (not even that interested in pellet porridge) preferring to forage when outside the run for grass, bugs etc or if inside would peck at corn on the cob, or veg hung up as entertainment. Her droppings were the same as your hen's.
I took her to the vet and he thought she may have a kidney infection and also noticed that her droppings had a large number of flagelets (thgink I spelled that right!) which are tiny amoeba like creatures. I asked what could cause that & he seemed to think the eating of sweet things like fruit could but doing research online I saw that drinking water that has been standing for a while (puddles etc which all hens seem to prefer!) can also be a cause.
He gave her ABs but they didn't seem to be that effective (though they were in tablet form and I don't think I managed to get much down her). He then gave her a different liquid broad spectrum AB for a week along with OREGO-STIM which is an oregon based herbal additive for their drinking water (I mentioned this to somebody else in a post a couple of days ago). This claims, amongs other things, to dry up their poos and it certainly seemed to help.
One other symptom my hen had was the colour of the poos - a very green colour. This may have been to do with her eating more vegetation but I am not so sure as some of her droppings in the last week or so have been a similar colour though nothing like as runny, even though her diet is more balanced now as she is back on her pellets.
I am just keeping an eye on her now and giving them the supplement from time to time. My gut feeling is that it is a kidney infection which possibly hasn't quite cleared up, that seems to at least partly answer the excessive drinking of water that happened initially (this has stopped now and if anything both hens seem to be drinking less).
In between vets visits she seemed to manage to maintain her weight and seemed otherwise well. I partly put this down to the fact that after the first visit he told me to give them the max dose of avipro (another additive) in their drinking water so that she at least was getting some nutrients in her (it was OK for my other hen to have this too).
I don't know if my post is of any help but your case sounded so familiar to mine I thought it may help to share! Hope your hen recovers soon.