GPU reballed, still black Screen

First off, you have to understand that reballing isnt a permanent solution and it is something that if it doesn't work the first time, you really don't try it again. Reballing is also something that isn't a gaurenteed fix. I have done reballing in the past and the method of baking the board in an oven can actually damage the board compared to a professional reballing. When you said that the DVI port was slightly coming of there could be many other small components that could have had parts of them melted. In my opinion this is a hopeless board and is way beyond repair. I would try and buy another logic board if you really want it fixed. If you don't want to buy a new logic board the computer could make decent mony on eBay as parts or just as a whole.

Hope this helps