iPod touch 1st gen failing to boot?

I have an iPod touch 1st gen which is quite old and is on it's third battery. However, it often won't boot with the back on, which suggests a short, but I have visually checked the connections and they all seem ok, and I have even covered them with tape, but I still get the problem. I then thought it may be shorting elsewhere on the board so I have covered other areas in tape which may be close to the edge of the enclosure, but I still have the same problem. Even if I do get the case on without it initially dieing, it only lasts a few days before the back has to be taken off, then it works again. I may just buy a new back as they only cost about £6, would this be the best solution?