Testing a Chromebook screen
Open the page in Chrome with your finger on the display and tap Start dead-zone test. On a Chromebook the biggest obstacle to a clean pass is the browser itself: Google lists swiping left to right as Back and right to left as Forward on the touch screen, so a long horizontal stroke on an ordinary page leaves it. Inside this test area those gestures are switched off, which means you can drag straight across the display from one side to the other.
The grid uses large cells (about 64 pixels). Sweep it in long horizontal strokes, top to bottom, and look for any cell that stays dark between two green ones. On a convertible, fold it into tablet shape for a second pass; in full screen the green cells from the first pass carry over.
Not sure the model has a touch screen at all? Touch the test area. No circle and a bar that says the browser reports no touch screen settle it.
When the touch screen doesn’t respond
Google’s steps, in order, checking the screen after each one: wipe any dust or dirt off the touch screen; reset the Chromebook hardware; and reset the Chromebook to factory settings, which erases its local data, so save your files first. If none of these fixes it, contact the Chromebook’s manufacturer.
For the hardware reset on most Chromebooks, turn it off, press and hold Refresh, tap Power, and release Refresh when it starts. On a Chromebook tablet, press and hold Volume Up and Power for at least 10 seconds. Google notes the reset might delete some files in the Downloads folder.
Sources: Chromebook Help: Use the Chromebook touchscreen, Chromebook Help: Reset your Chromebook hardware.