How to put operating system back on tablet

the tablet will turn on but the operating system is gone i gone to best buy to see what they can do but they said the system is gone did nothing to the tablet and i left it on the table and what happen was the screen had a different color and i touch the screen and it will shut off and turn back on and do the same thing tell the battery died so don't know what to do tried to factory rest nothing.

i even tried putting the same softwear back on nothing so if any one can help that will be great THANKS