@hunieboy yes, you do want to replace the battery. It may have used it's last bit of energy and now no longer accepts a charge. Anything like this "saw some black corrosion" needs cleaning. I suggest you remove your motherboard and clean it with some isopropyl alcohol. Use nothing less than 90%+To clean it I suggest you follow [guide|5825|this guide.] It was written for an Apple iPhone 3G but it is still pertinent to your console as well.
After that replace the battery, reassemble and re-evaluate. Post some good pictures of your motherboard before cleaning so we can see where there is any potential damage.
[guide|21499]
[guide|1301]
[guide|1297]