So it doesn't show any power at all? Are you using a FireWire connection? 3rd gen iPods do not charge over USB so having a USB cable connected won't supply any power. If you are trying FireWire but connecting it to your PC, you may want to try the wall adapter that Apple originally shipped with the iPod.
Even if you do get a FireWire cable for it, I'd bet you'll still need a battery replacement. The 3rd gen batteries weren't too great to begin with and they're from 2003, almost 10 years old. It should work just fine while connected to FireWire though, assuming the hard drive and logic board haven't died.
Not sure about the UK but I believe in the USA Apple will offer you 10% off a new iPod with the trade-in of an old model. By now, Apple considers the 3rd gen obsolete and will not repair it (if it is in fact broken), and I don't believe they offer battery replacements for it either.