here are the steps for checking your tama's screen. these worked on the first gen tama so not sure if they'll work on a tama plus, connexion or connection. maybe some people can test this out on their pets just before they hatch them or right after one dies. REMEMBER!! This resets the Tama completely!
(had this copy with no original source recorded... Not sure where it came from)
The test mode is available to make sure all the pixels and icons are working. To start the test mode hold down the left button while pressing the reset button on the back of the case. The screen will then be totally black since it will be displaying all pixels at the same time. You can then press the middle button to make every other pixel be displayed (checkerboard pattern) with half the icons being displayed. Then press the right button to alternate which pixels are displayed (checkerboard pattern opposite of the first). Then press the left button to display an empty box (just the outside pixels of the screen). Press the middle button to get the egg to hatch another pet.
You can try running through this process multiple times to see if your screen shows the problem you described originally... If it does, return it as defective. If not, maybe its normal (?).