Restart the TV. Even in Game Mode, there may be a bug that doesn't put the TV in Game Mode. For example, the Sony X800H has an issue where it has high input lag if you turn on the TV and it's already in Game Mode; you need to switch it out of Game Mode then back in for it to work. Auto Low Latency Mode not working. Check to see if it supports it.
From your description, it sounds like it has to do with your input labels. To re-activate those inputs go to your TV’s menu under "setup". Then select "input label" and press enter. Once you enter the menu, select the inputs you want to activate (in your case input 1 and 2) and use the side arrows on your remote to select a name. Then pressStep 1: Unplug any devices connected to your Sharp TV. Step 2: Disconnect the TV from the power. Step 3: Press and hold the ‘Power’ button on the TV for 30 seconds. Step 4: Wait another 10 minutes to allow the TV to fully discharge. Step 5: Plug the TV back in, reconnect all devices and turn it on.