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Hi Alex, welcome to the Sony Forums
How old is the camera?
It's possible that the contacts have become damaged, short-circuited or corroded, or perhaps (less likely) a fault with the charger. Have a look at page 163 of the User's Manual and make sure you're charging according to the instrcutons there: http://pdf.crse.com/manuals/4000946111.pdf
Cheers
Mick