My laptop (Winbook X4) was dropped and landed on the area where cord goes into computer. The area inside computer was broken. A repairman superglued it, and it worked for awhile. He said I should probably buy another computer if the glue didn't hold. The ac cord cannot make contact in order to charge battery. Would a docking station recharge a battery? How do they work? I don't know anything about them. Would there be one available for my computer? I can't seem to find one by searching the Internet.

Before you do anything are you covered for damage under your household insurance for replacement ie new for old.
You dont say where It was damaged but by the sound of it must have happened in your house !!