Should I switch the iphone battery?

So my iphone 4 won't turn on at all even when in the charger but it shows the connect to itunes symbol and won't let me restore should i try getting a new battery and charger?

I had the same problem last night working with a contact groups issue on my iPhone4. I had to do a full restore. This issue came up during the restore. The apple care rep had me switch to a different USB port. That fixed the problem.

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