How would I tell if battery is shot vs. bad dc-in board?

My 12" PowerBook will run for about 20-30 minutes on battery but then the screen starts flickering, and after a few minutes of flickering, it suddenly goes to sleep without any other warning. My battery only has 91 cycles, so how can I tell whether the battery has gone bad or if the problem is something else more fatal like a bad dc-in board. The current maximum capacity of the battery is supposed to be about 1/2 of its original capacity according to System Profiler, but it will only run for about 1/8 to 1/6 as long as it used to. My PowerBook otherwise works great and has Leopard, maxed memory and an upgraded harddrive, so I really would like to keep it going. It is so superior to a netbook and much more capable than an iPad as far as doing real work is concerned. It works totally fine when plugged in but I hate to gamble and spend $100 on a new battery if the electronics are shot.

Your battery could be shot with only 91 cycles if it's plugged in all the time. Lithium batteries need to be used, and go through full discharge/charge cycles in order to stay in good working order. Apple says the minimum is one full charge/discharge cycle a month to maintain the battery.
If it works fine on power when plugged in, then your DC-in card is working fine. Replace the battery and read up on battery maintenance on http://www.apple.com/batteries/ and http://www.apple.com/batteries/notebooks.html
One source of replacement batteries is http://eshop.macsales.com/shop/applelaptop/batteries/PowerBook_G412

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