OK Andy, I am under strict orders not to be a wireless doorbell salesman. So first things first. You may simply have a broken wire going to the bell or the button. I would check continuity there first. Pretty easy to replace wire. Another option might be a big brass door knocker. I got this tip from Dodgeman and in fact, thats what I use. Door knockers never short out and most folks know how to use them.
Your doorbell should be repairable and as a last resort, if all else fails, you can listen to Steve's recommendation. But belive me, you will be forever scorned if you take the easy way out and go wireless. (If this seems confusing, you would have to see yesterday's post on "another doorbell problem).