For starters, you definitely don't need to spend over a thousand to get a solid performing gaming PC.
As for securing funds, the tried and true method of mowing lawns in the summer and shoveling driveways in the winter worked well for me when I was young, although it's a slow process of gaining money. Ask for gift cards / money on gift giving holidays and slowly build up the money to make it happen. It might take a while but I think you'll find it will be very worth all the effort.