|First off, have you tried using a different charger or outlet?|
Make sure you are using the charger that came with the camera, or at least one that is rated the same (DC 5V, 550 mA - from the user manual)
Was the camera completely dead when you tried to charge it?
The manual says that it should take approximately 3 hours to fully charge the battery. Sometimes, when the battery is completely dead, the device will require you to completely charge the battery, and will not turn on if it is partially charged.
Have you tried taking the battery out, trying to turn it on, then putting the battery back in? It sounds kinda silly, but it discharges all of the electricity from the system, and can help to sort of 'reset' it.
If the camera can still be turned on, but just cannot be charged, make sure the setting 'Charge by Computer' is turned off.
According to the manual, quick flashing of the green light means either the charger is not properly connected, or the battery has failed.
Do the above steps first, but if they don't work, you may just have a faulty battery. In which case I suggest you contact the manufacturer and get a new battery.