OK, what you are saying sounds more like it won't turn on, not it won't charge.
So, if you actually do mean it won't charge (but turns on) try charging when it is off (not sleep or hibernate but off). If it charges then, but not when on, then it is most likely the charger that is malfunctioning and needs to be replaced.
However, if it won't charge no matter if it is off or on, then I would start by replacing the battery. Just really consider an OEM battery, as many aftermarket ones just won't work the same.
Now, if you mean that it won't turn on, try the following and see if it will turn on...
1. Unplug your charger cord.
2. Remove the battery.
3. Press and hold the "Power" button for 30 seconds.
4. Now plug back in the power/charger cord.
5. Now put the battery back in.
If this doesn't help, then test the power cord to see if it is good. Either try your cord in another device, or try another devices cord in your laptop. You may also want to try charging it when the device is off, rather than on. If it works then, the cord is probably the issue.
Should that not be the problem, then check the battery to see if it needs replacing.
If you do not feel comfortable doing this yourself, then I would try a local tech.