To make sure that firmware is not causing the LCD to malfunction run the On-Device diagnostics App in your phone and tap on LCD White test. You can test the LCD in five different colors which you can use to check the pixel integrity. Here is the list of the colors you can check your LCD with.
If you don’t know how to access diagnostics app in Nokia Lumia 610c read this post Use Diagnostics App in Nokia Lumia 610C. The colors will change when you touch the screen.
If that does not work check this Nokia Lumia 610C LCD problem troubleshooting flowchart guide. It explains step by step how you can test and repair your phone. I have also marked the parts mentioned the diagram.
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