Clean the contacts the best you can, use anything to the scrape any oxidisation from the contacts, carefully!!
if they are slightly sprung loaded at all you can try gently prising the contacts out a little, but careful again, too far and they pop out and it gets bad!
yeah you can replace the port on the lappy, if you can find a replacement part to buy and are handy with a soldering iron (and are capable of taking a lappy fully to bits!) and to pay someone to do it is gonna be pricey!!