Inverter do not charge for a couple/few reasons, one, the battery it's trying to charge has a too high internal resistance, and the sensing part of the inverter, is unable to properly detect, and charge the battery. The second is where the actual charging circuitry itself, has a failed component or the like, in the output/input control circuitry, that must be fixed, and thirdly, the CPU, controller, has faulted, or the sensors feeding it have failed. To have any chance of a repair one simply must obtain a thing called a service manual, this will give you troubleshooting steps as well as a circuit diagram too. However these units are very sophisticated, and home repair isn't really recommended. Also remembering you are indeed dealing with lethal voltages so all safety precautions must be undertaken.
Operations manual below.
http://powertool.manualsonline.com/manuals/mfg/xantrex_technology/dr1512_dr2412_dr1524_dr2424_dr3624_dr1512w_dr1524w_dr1512e_dr1524e_dr1548e_dr2424e.html
Support center below, try contacting them direct and get a service and repair manual.
The best way to fix it, in my opinion, is to contact the manufacturer,and ask for a local repair agent, then when there ask for a "Quote" for the repair before proceeding, this way at least you will be able to make an informed decision.
http://www.xantrex.com/support/web/id/1088/support1.asp
