Here is the owners manual for your device: http://cc.cnetcontent.com/inlinecontent/mediaserver/test/105/b09/105b09fe00364be78e1a4dbfd340bc75/original.pdf
You say that a little red light comes on like its charging, however, a solid amber light indicates that the charger is disconnected, and that the battery has a charge between 5% and 20%.
I would recommend using a multi-meter to test your charger.
As for it not powering on, you should try to remove the RTC battery, the main battery and the charger and hold the power button for about 30 seconds. After reconnecting you can see if it will power on.
If that doesn’t work, you will need to test the power-button and the motherboard with a multi-meter, it could be that the power button broke, or that the board isn’t getting power.