Install the pavucontrol application, start it and go to the “Input Devices” tab. Unlock the channels (click the keylock icon), then mute the right channel while keeping the left channel at the volume you want.
If the internal mic is now working correctly, you have an inverted internal mic, so that your right channel cancels out the left one. (Why the hardware is constructed that way is beyond me.)
This seems to be most common on Acer Aspire laptops, but I’ve seen them on other laptops as well, and fixing these are more of a long term project as they are non-trivial kernel patches. So far I’ve created a patch for Thinkpad U300s. Anyway, I would like to track the remaining ones in bug 1002978, so please add your system there according to the instructions.