Will a iPod Touch 3g digitizer work for a 2g iPod Touch?

I replaced the original touch screen after ripping the digitizer ribbon when I opened my iPod Touch 2g for the first time...

I have a similar problem posted previously in this forum that one of the three soldering points for the iPod touch battery...

I just joined this forum and did this myself on my 2nd gen iPod touch and it is my believe that one of the three battery connection or solder points, specifically the middle one, does not have a solder plate or line underneath it like the other two, which were very easy to solder back on, but the middle one gave me the impression I overheated and removed it, but there are no traces of a plate in the middle, not even at the old battery's middle connection point.

Hello, I was doing a search and did exactly the same thing as what the poster of this question did. I realize this question is about a year old but checking to see if the original poster did get it fixed or if he took it to someone to get fixed, but what did that person do about getting a new solder point elsewhere on the board? Maybe use one of the tiny circular test points as George Mathew suggested, and if so, which one? And just a side comment, I examined the middle connection of that battery cable and it just seems like that one is soldered differently from the other two (on either side of it), as the ones on the side easily came off with the same amount of heat applied to the middle one and the middle seems to have its contact point above the circuit board because when I examined the old battery terminal, there was no residual solder or what looks like a foil contact on the bottom like the other two connections on the sides had. Sounds like an Apple manufacturing process designed into it so...