There is a fella in Ca that for a pretty small fee will fix the contact issue on the Garmin 305 and will also install a battery with a much longer life for another small fee. It sounds like the OP's might be a different issue but for anyone else I can probably get his contact information if it's needed. He fixed a friend of mine's 305.

I have both the 305 and 705 and very happy with both-although I stopped uploading rides a couple years ago!