Hi,
Ensure that the main power switch (located on the side under the flap is in the OFF position, when trying to charge the unit.
If it is and you still get no charging indication with the charger connected to a known working power outlet try the following:
Connect another known working '''12V DC output''' charger (specs are on the charger) with the ''correct size plug (centre is the + pin - most are but be aware)''. If the light comes on your 1st charger is faulty. If not you either have a faulty battery or a faulty charging circuit in the speaker .
If the speakers work when connected to the charger then the problem is most likely that the battery has failed. They do have a life expectancy. Here is a link for a replacement battery http://support.tdkperformance.com/article/AA-00413/22/Rechargeable-Battery-Replacements.html