Water-damaged iPhone 5 will not stay connected to computer.

Hi. My iPhone 5 went swimming with me. I've left it in rice for a week, cleaned it obsessively, replaced the battery twice, plus replaced the dock connector. When I power it on, I get the temperature warning, and the battery drains super fast until it dies (touch screen is also unresponsive).

I would just like to get it to stay connected to iTunes to restore it and clear my info. However, when I connect it, my laptop gives the connected device sound, iTunes recognizes it, then it immediately disconnects from iTunes and my computer.

Anyone have any ideas here? Do I have any options?