Yes you can fix the charging port on the Mega. The part is not that expensive and can be found online. Its an easy fix as well.
Charging port replacement guide:
[guide|59743]
Dont remove the board you can just do the charging port
Part that you would need:
http://www.ebay.com/sch/i.html?_from=R40&_trksid=m570.l1313&_nkw=galaxy+mega+charging+port&_sacat=0
Search for charging port on Ebay and you would be able to find it
You can also use [http://dashrepairs.com|cell phone repair store nearby] to find someone that would do it for you.