I have a leaking waterline under ground and the pipe is very rusty and corroded. How can I repair this without digging up my entire yard and replacing all the pipe?

Yes! There is a way. You can have the pipe relined, This is just one of many companies that do this. Expect to pay about as much as you would if you dug it up and replaced it. Check it out at; Epoxy Pipe Lining (http://www.toolbase.org/Technology-Inventory/Plumbing/epoxy-pipe-lining)
Good luck, Tom