..personally I would have went with the energizer bunny. LOL.bought a new Duracell battery.
Seriously though, take some time and perform some diagnostics before spending money. By the boot I assume you are talking about the boot between the carb and the cylinder head. Get a can of WD40. With the bike idling, spray the boot, the connection at the boot to carb, then the connection at the boot to head. If you do have an air leak the rpm will change while idling. The WD40 will temporarily seal the air leak (about 3-5 seconds). If not you have other issues. It's kind of messy, but tells the story if that is the issue.