If that battery is 2 years old, it was due to soon be replaced anyway. Whether the laptop was on the AC adaptor or not, makes no difference. The battery will gradually "die", your operating system may suddenly report it to you as if it "just" died, but truthfully the battery starts dying the moment it is used for the first time.
My $200 Black Friday special Toshiba is now 6 years old and the battery last for about 3 minutes, that's enough time to safely shut it down in an emergency and I agree with the other poster that says replacment batteries are a racket/rippoff-way overpriced ! Adaptors being warm is perfectly normal and did you know that an ac adaptor plugged into nothing but the wall recepticle still uses electricity ? Unplug those unused ac adaptors and save your money ! Look about-you could have as many as 10-12 of them plugged in !