Also, just a tip that worked for me..instead of trying to remove the old battery with the solder tip trying hard not to short or bridge the terminals, I just snipped the old battery ribbon cable back about an inch or so from the solder joints with scissors. Then with a grip on the leftover piece of ribbon I just quickly applied the tip to all three solder joints and lifted it off easy. (I am sure this is not what is standard practice, but with the battery snipped off and out of the way, I didn't see the a problem with bridging the terminals all at once, since there was no battery voltage to worry about.) Anyway, it worked!
I had a problem with mine after the battery was replaced. I would turn it on and just get the sliver of red for the battery, and it would not boot. It would work fine until I pressed the LCD assembly down into the housing, and then the battery went dead. What I observed was that the LCD ribbon cable that runs under the battery to its socket was quite stuck to the back of the case when I tried to remove it. This left a bit of the insulation from the cable stuck to the back of the housing. After replacing the battery it would work fine till I pressed the LCD down, and then it would short out. So I lifted the LCD assembly again, lifted up the LCD ribbon cable and put a inch and a half piece of black tape down underneath between the cable and the housing. After reassembly it worked fine.