Spoke nipples are cheap (about $0.12 from a reputable online source I use). That equates to $6 for 50 which should be more than enough to fix the rear wheel. If you have the time, it could be a great learning experience and worst case you are out $6.

For an inexperienced wheel builder, your best chance at a good final product will come from completely detensioning the whole wheel and working methodically back to a tensioned and true wheel. With that in mind, now would be a good time to completely disassemble the wheel and assess the rim. If the untensioned rim is fairly flat and round, you stand a good chance at building a decent wheel with it. If you find spots where the rim is out 1/4" or more in some direction, toss it in the trash and either buy a replacement or a whole new wheel.