DIAGNOSIS This is a known issue with capacitive touchscreens in dry, cold conditions, compounded by possible static electricity buildup. Low humidity (common in winter with heating running) reduces the screen's conductivity, making it less sensitive to your finger. It's the device, not your wiring.
FIX The immediate fix is to increase local humidity. Try breathing lightly on the screen to add a tiny bit of moisture—it sounds silly, but it works temporarily. For a longer-term fix, consider using a small room humidifier in the area. You can also try rebooting the thermostat by going to Menu > Settings > Reset > Restart. This clears its memory and can sometimes help with sluggish performance.
IF THAT DIDN'T WORK If it's completely unresponsive, you can perform a hard restart. Carefully pull the thermostat off its wall plate. You'll see a micro-USB port on the back. Plug in any standard phone charger USB cable. This will power it directly and bypass the 'C' wire. The screen should wake up. While it's on USB power, go to Settings > Reset and choose 'Restart'. Then unplug the USB and re-mount it on the wall plate. This full power cycle can clear deeper glitches.
HEADS UP Don't use liquid screen cleaners or press hard on the screen. A dry, soft microfiber cloth is all you should need for cleaning. The screen is durable, but abrasive cleaners or excessive pressure can damage the capacitive layer.