3.Wait 2 minutes, Now put battery back and plug-in Ac adapter.
4. Start your laptop.
See if keyboard operates as normal ?
If not, do exactly same as above but before putting battery and plug-in ac adapter back in, remove the keyboard.
After removing the keyboard, see if there is any dust in there. Clean keyboard port and reinsert the keyboard cable back-in.
Do #3 after that.
Also try to boot into safe-mode and see if keyboard works there or create new userprofile ( which i doubt you can't since you are unable to sign-in/log-in i guess?)