iPad 2 will not turn on after Update 6.1

I've read a number of discussions on the issue, but have yet to find a solution. I am using an iPad 2 (version A1395).

I tried updating to iOS 6.1 over WiFi. It seemed to download well enough, but when it got to the installation, it kind of fried my iPad. It will not turn on. I have tried all of the following:

1. Pressed the Home button (also tried holding it down).

2. Pressed the Power/Sleep button (also tried holding it down).

3. Pressed both at the same time (also tried holding it down).

4. Held the Home button while connecting to a PC via USB.

5. Held the Power/Sleep button while connecting to a PC via USB.

The only action that gets any response from the iPad is plugging it into power brick via USB. The Apple logo will appear briefly, indicating that it's powering on, and then it shows the "Connect to iTunes" graphic. Nothing more. If I unplug from the power brick, the screen turns off. Plugging it into a computer after that does nothing.

Any ideas?