Have you tested your hardware ? HDD or SSD not broken ? RAM not broken ? RAM you could run memtest and see if it gives any error, for HDD you have couple of different ways to test, but i always unplug it, and test it external on an other pc with hdsentinal, some people will tell you even if its at 98% its still good, but even then it could be better to replace it. If you have an other HDD somewhere just test if it works with that one.
Did you try take a backup and reset the ipad ? i highly doubt this is a screen problem, more like a software problem, also it could be a defect homebutton in the meaning that it will work but if you click it it wil stay clicked giving you everything to see ( siri and so on )