First of all you should test that your phone’s firmware is not causing this problem. To do that you need to access On-Device Diagnostics Tool in your mobile phone. If you don’t know how to do that read this guide How to Test Diagnostics in Nokia Lumia 610C.
After accessing Diagnostics App go to Touch Test, you will see a blank white screen at touching the screen a trail will be left on the screen. If that works then you need to flash your phone.
If that does not work then study this Nokia Lumia 610C Touch Screen Problem troubleshooting flowchart. Follow this flowchart and hopefully your phone will start working again.
If you have further questions please don’t hesitate to leave a comment.
Note: Every repairing solution posted here is tested by at least one member of our team. Use the information available here at Your Own Risk. We are not responsible if any harm comes to your device during the repairing process