The fuse on the battery itself if busted up. Will it hurt the vehicle by not replacing it?

I'm not sure what the "fuse on the battery" is. I do not think it is a "factory" installed item. Some folks add cabling and wiring for aftermarket components, such as alarm systems or audio units. Perhaps it is one of these items -- even if, and likely inactive -- that has a "busted fuse". Your starting issue sounds like something else that will require some hands on troubleshooting. www.repairpal.com/repair-shops