Yes, I'd say that sounds like a dead battery. If you take it out and place it on a flat surface, can you rock it? Exhausted batteries often swell and that would be conclusive proof. There have been various issues with Samsung batteries and they've been pretty good about replacements. Vodafone have too, but Samsung are more likely to have stock, so going to them via the Support tab of theie UK website, would probably be quickest.
Allowing your battery to go flat can also shorten its life so, if you've been doing that, it would be a good idea to stop. I doubt Samsung will argue about a replacement, though.
