White screen of death / capacitor next to gpu blown out?

Depending on te size of the capacitor (Could you post a picture?), it may be impossible, unless you have amazing soldering skills. I've successfuly done component-level repair on game consoles and computer hardware, but never on moble devices. The smallest diodes I've ever been able to successfully replace were around 1mm in size, and I've been doing this stuff for years. You would also need a soldering iron with a very fine tip.

You really can't use a Iron on the SMD's. (You can but It needs to have thermal controls). Also capacitors don't blow without a reason. There is a short somewhere else. Probably corrosion bridging a trace. To remove You just need to remove the soldier with wire brade. Re tin the cap you remove and put in place. Heat one side pushing the part down heat the other side. Should be pretty easy.