Casio exilim ex-Z750 camera wont

Have you made sure the battery is still good? Even if the battery looks like it's charged (via the charging cradle) it may not be holding the charge.
So first, test the battery. How? Easiest way is to go to a camera store.
Before that, try removing the battery from the camera. Then reinsert it. This will reboot the camera, just in case that is the problem.
Finally, assuming the camera has not been dropped and that it is a mechanical or damage problem, download the latest firmware update.

It is either the charger not working correctly, or the battery is shot. The batteries for these cameras do not last all that long..so 9 months and I would think it's time for new battery. Order a new one off EBAY...if you buy one in the US...you will pay quite a bit more than if you purchase from China. I have found that not all batteries you buy will work...so it is better to buy from the US where you can return it much easier if that becomes an issue.