Leakage from the battery will often form corrosion on the legs and sockets of the CPU closest to the battery. Extremely rare but also possible is the bad battery causes a short. Carefully cut the legs on that battery and get it out before it does more damage.
If you're handy with tools and fine details, pull the CPU, carefully clean the legs with an eraser or very very fine sand paper (600 grit or higher). Next check the CPU socket closest to the battery. These types of sockets are not easy to clean, often I just replace them. But if the corrosion is not terrible in there, you can use a sewing needle to carefully scratch at the inside of the sockets to clean the worst part of any corrosion. The sockets should look silver, not green or dark. After it's all as clean as you can manage, slowly replace the CPU being careful not bend any of the pins.
I hope you get it running again.
Plaz
