Have you tried a second known good MagSafe charger yet? Have you tried resetting the SMC?
I would give this gem of an app a try, it will give you the details of your battery and the charging of it: coconutBattery. Post a screen shot so we can see whats happening here.
How does your MagSafe charger look? Is the cord damaged in any way? Cuts, bumps or twists? How does the connector look are the pins shiny? Is the plastic melted. Looking at the system how does the MagSafe connector look here? Are the contacts shiny? Is the plastic melted. Do you use a surge suppressor? Or a UPS?
Why I ask these questions is often the MagSafe charger causes damage to the system. A cord that is damaged is likely to short out. A system which is powered all of the time can get damaged from a power surge.