In trying to fix my unresponsive touchscreen, I have read from various websites that I should perform a 'device reset' or...

The problem you are having could be due to a number of reasons, including a faulty cable, battery, or Micro USB board. Please visit the Nexus 7 (2nd gen) troubleshooting page for possible solutions to your problem.

Though the options are limited, there are a few currently listed on eBay. A search for 'nexus 7 sim card tray' will get you to them. Additionally, you might choose to contact Asus directly.