Joe, I would suggest upgrading the putter. I personally like the ones that have 10,20,50, 100 increments. If you are serious about this game, then it's a "no-brainer".
However, I do know a Tour Legend on this site that still uses a starter putter and has a 56.xx avg. I just don't know how he can make those putts with it! (lots of practice I'm guessing) ;)
Dan