Is my Battery in need of replace?

I have a 3G that is 2 years old. Lately my phone has been crashing (full shutdown) every time i go on email, or Safari ( and maybe other places). I took it to the Apple store and they reset it to see if that would fix it. It did not. I told them the battery goes dead in about 20 min. They hooked it up to a Mac laptop to test it. They said the battery tests ok. I think they wanted to sell me a new phone more then anything. This was happening before I updated it (and after) to 4.0.2. It It seems to work fine when I plug the phone into a power outlet.

My question is: Could this be the battery? Should I spend the money and replace the battery or could I be putting money into a dead horse?