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Help Shut down problem

My Samsung Galaxy W shuts down whenever I have either 3G or Wi Fi switched on. If I switch on whilst connected to a charger there is no problem, once I disconnect then it will shut down within 2 or 3 minutes of activating 3G or WiFi. When I manage to get it to restart, it indicates that the battery is flat even though it may have a ful charge before shut down. I have restarted it whilst connected to my lap top and had 2 messages - first said that the battery was fully charger and should disconnect, whilst the same screen is showing 40% battery charge.

I have backed up my data, done a factory reset and still have the same problem.

Any ideas what is the cause and a fix for it? I am a novice with phones by the way so any technical stuff will need to be explained.

Thanks in advance.
 

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