Hello jneuhard,
After reviewing your post, it seems like the battery icon is yellow even when fully charged. This can happen if you enable Low Power Mode in the Settings even if fully charged. Since part of the screen is not responding to touch, you may need to take to be evaluated for service. The third article may help to get the iPhone recognized by the computer.
Restart your iPhone
"When Low Power Mode is on, the battery in the status bar will be yellow. You'll see
and the battery percentage. After you charge your iPhone to 80% or higher, Low Power Mode automatically turns off."
Use Low Power Mode to save battery life on your iPhone
If your computer doesn't recognize your iPhone, iPad, or iPod
Please don't hesitate to let us know if the steps resolved your issue or if you need additional assistance.
Thank you for using Apple Support Communities. Have a nice day.