You'll need to carefully work the pathway from the MagSafe charger to the logic board. Making sure each part of the circuit is working correctly.
The first step is a good inspection of the connections. Review this Apple T/N: Apple Portables: Troubleshooting MagSafe adapters. Hopefully you have a bad connector if you do follow this IFIXIT guide to replace it: MacBook Pro 15" Unibody Late 2008 and Early 2009 DC-In Board Replacement. If the connections look good you'll need a volt meter to measure the voltage as well as schematics and board drawings for the system
Do you have access to the needed tools and are you up to doing the needed tracing. If not you might as well find someone with the skills to do it.
But before you go to deep here keep in might this system is no longer supported by Apple so its limited on what it can run for OS's & apps. So make sure you don't over spend here.