Was the unit new... computer, charger, battery?
Is there a chance it may still be under warranty? Most sales come with a 12 month warranty period if not longer.
Has the laptop or the charger unit been dropped or subject to great amounts of heat?
There are lots of things that can go wrong with batteries, sealed, Gel and liquid types.
The plates can be affected by heat (which is the major cause of any failure).
If, for example your laptop had been in front of a window during the bright/heat of the day, say inside a car, then the components internally warp and can short out.
Most batteries consist of several cells each with the same voltage to make up the total of your battery's total voltage. eg 6 cells @ 2 Volts = 12 volts and it only takes one cell to fail and the whole thing becomes faulty.
There are modern batteries that have lithium, magnesium and alkaline features in rechargeables and rely on the charger unit to supply the correct voltage, regulated by the charger in "AMPS" or "Milliamps", any faults in the regulator can affect the chargeability of your battery. A sudden impact, say from being dropped,could render your charger ineffective.
I suggest you try anther charger of a suitable type, if you can, to see if that is the source of your problem first.
Try your charger in a friends (Compatible) computer laptop, or have it tested at a reputable dealer.
You might be able to get a loan of a battery to use in your laptop, to see if the battery is at fault or the problem.
After that, things like connections to the laptop and into the wall socket should be examined.
Hope this gives you some insight as to where to start.