I would say your best route would be to backup all the data and just a new machine and sell the old one on ebay as is. Replacement laptop motherboards are so expensive it generally isn't worth it (unless you have an extended warranty or something). You might be able to find the same model on eBay with a good board (and say a bad LCD) and swap the board, if you are feeling like a real go getter. But my advice is to just ditch it, oh and ditch Dell too
