It is not that hard to recap a Classic II/Performa 200 logic board. The problem is that space is very tight and you might not get the iron in place to solder properly. But if you have the money, it would be better to send it to Uniserver, he has a hot air soldering station for this kind of work. He'll get that mad  puppy howling in no time! Discuss with him about repair, parts and shipping costs. I'm not discussing prices, but from what I seen and heard, he's done excellent work for the price he charged.

The Battery in Question is a red and white/silver battery with MAXELL on it. They tend to blow up and spill their battery acid and destroy boards from massive corrosion.  Other batteries do this as well, but not at the scale the MAXELLs do it on. Since the Mac IS DOA anyway, you should open the case remove the battery (regardless of name brand) and chuck it immediately if it has not corroded. When you get/repair the board, put in a new battery.

Good luck on the bidding.