The main point of building a server is precisely to have it running 24/7, so that you always have a remote backup available, plus any other things you may want to put there.
I would reuse the old hardware for that. Since servers essentially don't need to be that powerful, more for a home one, and you can put good use on that box. 6 years old is not that old anyway, if properly cared it can server well for much time. The only thing I might be concerned about failing is the hard disk which has mechanical parts, so having a good backup would be good idea. Everything else may last years.