Buy a new laptop charger. It sounds like its faulty. To buy a laptop charger in shops is very expensive. I personal buy laptop chargers from ebay, as the tend to only cost around £10. Just search ebay for the same model number/laptop type and make sure that the voltage out is similar to that of the one your replacing. All information is on your battery for voltages.
Once you get your charger, try it and see if it solves your problem. If it does not then its a completely different issue.