Lenovo laptop cpu speed down to 0.5 GHz from 3.0 GHz normal speed when battery connected and plugged in to ac power

This problem of mine has nothing to do with power options. I really can not understand what is going on. When the battery is connected and the laptop is plugged in to ac power, laptop cpu speed is so slow. But if I shut down the laptop, remove the battery, plug in the laptop to power and boot up(without the battery of course), the speed is back to normal (3.0 GHz). I have noticed that the battery is not charging when connected to the laptop. Is this a battery failure? Have you ever seen this problem before?

Question by Nick_K on Super User, licensed CC BY-SA. We show a short excerpt and link to the original thread as credit.