Lets see if we can collect some diagnostics. Download this app: coconutBattery. Post a screenshot on what it shows here in your question (edit it).
I would also recommend you reset the SMC to see if that fixes things. Follow this Apple T/N: Resetting the System Management Controller (SMC) on your Mac.
Also take the time to clean both the power adapter and the computers MagSafe connectors. Get a cotton swab dampened with some high grade isopropyl alcohol (85% or better).
The charging circuit is having problems! Note the zero charge 0 mAh for current charge.
You may need to clean the MagSafe connector contacts on both the power adapter and the system. Use a cotton swab dampened with high quality isopropyl alcohol (85% or better). You may need to replace the DC- In Board. If your power adapter has a damaged cord its time to replace it as well.
The batteries condition is not good either. You're near the max charging cycles (967) designed for 1000 cycles. Its time for a new battery.