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I think you need to replace the volume button module.
Make sure that all cables are plugged in, and that no cables are damaged. If you used a heat gun, it may be possible that you accidentally fried a cable while melting the adhisive.
The Logic Board is fried. You need to replace it.
I believe you may have either left a cable disconnected, or you damaged the LCD. Check inside for any disconnected cables, and it there aren't any, order the iPhone 4 LCD replacement.