Well, the sad day came today when I went outside to muck out my hens and found one of them curled up in the corner of the run, dead as a dodo. Thank goodness my 4-yr old was at her grandparents' house and the 1 yr old is too little to care/notice. But I have no idea why my chicken died

She was an ISA Nick Brown (or something like that) and she seemed absolutely fine and happy. When she was last in the garden on Monday afternoon she was pottering around, scratching the ground, pecking for worms, etc, etc, and seemed absolutely fine. The other chickens are fine - they have plenty of food/fresh water/fresh bedding every day. One thing that DID happen at the weekend - my 4 year old said 'Mummy, Beans has got blood on her bum'. Well, I watched Beans pecking around and she seemed perfectly happy and I thought her bum feathers were just a bit mucky so I didn't worry about it. And now she's dead. I took a look at her vent tonight and the feathers around it really are very bloody - the vent itself was very red and raw, but I couldn't see any obvious sign of any kind of egg blockage (although I didn't look too deep inside!).
If anyone has the stomach for it, I uploaded a picture - it's quite yucky and it is here: http://www.mediafire.com/?9o8rn67ak6r9lhz It looks worse in the pic than it did in real life - there's a big clump of bloodied tail feathers but the actual vent is above the clump, sort of to the right of the pic, and was not quite as messy as those tail feathers.
I feel like I've let her down and should have taken a proper look when my DD told me to! And what's worse, she was the nicest chicken. The other 3 are kind of narky, so Beans will be sadly missed. I can't pick the others up for a cuddle!! Presumably it would be worth me checking the other chickens' bums?
Thanks for any advice. Sorry for such a long post and such a yukky picture!
Emma