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Sounds like the problem is with the battery itself, not the charger.
, About This Mac, More Info..., Hardware, Power, Battery Information will provide a snapshot of battery health:
(This screenshot is from OS X 10.6.8 'Snow Leopard' on a MacBook with an aftermarket battery.
The exact display on your OS X 10.5.8 'Leopard' screen will be somewhat different, but contain similar information.)
If you have a MacBook with the removable battery you can get a new third party battery fairly cheap on eBay. Every MacBook from 2006 through Mid 2009 except the Late 2008 Aluminum Unibody use the same battery.
Or for $129 from The Apple Store http://store.apple.com/us/product/MA566LL/A?mco=MTY3ODQ5OTY