Corners are cheap, like under $15 bucks. My first move would be to buy a new one and cut the face off of it. This could be done in a table saw with a panelling blade. Loud as hell to cut this way, so eye and ear protection is a must. Now you have a nice piece to overlay on the corner. Clean the old one good and use an adhesive caulk, I prefer clear "Lexel" and a lot of masking tape to hold it on place until the glue dries. I have done this sucessfully for hail damage, where the product was no longer available, and the homeowner had very few precious scraps that he saved in the attic. Option two is to replace the corner. Cut the old one with a razor knife, right down the outside edge. this will allow you pull it apart and pry the nails out without pulling all the siding off, because you are going to avoid that at all costs. Now you need a siding zipper tool. this is an odd little hand tool that will unlock the siding. The goal is to gently pry the siding up and get a few nails into each each nailing flange of the new corner. Unless you live in a wind tunnel, you should be OK with 4-5 nails on each side. Pick a hot day, have a buddy to hold the siding bent out of the way while you renail, and you should be fine. Vinyl is hung on the nails, not nailed tight. you need to be able to slide a dime behind the nail head as a feeler guage. If you don't have a dime gap, and the nail head is tight, the siding will buckle and look like shit when it gets hot. Good luck.