Almost all batteries can be replaced, just some not so easily.
NOTE: Before doing any physical work on the laptop, make sure it isn't still under warranty. If it is, and you open it up, you will void that warranty, so you should contact the manufacturer about any work. If it isn't then consider the options below.
Was the laptop banged on something or dropped? Even a small distance? I ask because this can jar the battery and cause it to not connect correctly leading it to not charge. You would have to open it up and check for any 'wiggle' room between the battery and the connections, as well as, any bent or damaged connections.
If it isn't the connections, then you would have to look into replacing the battery.