Broken Digitizer or broken Lcd screen?

The LCD underneath the digitizer is damaged, probably by someone dropping it or pressing down on the cracked screen...or moisture/dirt getting into the crack.

A replacement LCD and digitizer will probably cost around $40 just for the replacement parts. If you don't know how to replace these yourself, you're looking at around $30+ for labor, if you go to a locally owned repair shop, depending on where you live.

Don't go to places like Best Buy or Walmart. They might give you a "good" deal, but they often install unwanted bloatware and data tracking software as a "bonus", and their technicians are much less reliable than those at mom-and-pop businesses, where mistakes really matter.

Depending on how much you paid, it may be cheaper to get a new tablet, unless you're comfortable with changing out the LCD and glass yourself—which I do NOT recommend if you have no phone or tablet repair experience, as its fairly tricky and there's a high chance of accidentally damaging something and wasting your money.

If you decide you buy a new tablet, you can sell your broken tablet for a few extra bucks on eBay or at a local repair store. If you decide to throw it out, be sure to recycle it properly, as circuit boards contain valuable and environmentally toxic metals.

Best of luck to you. (And insist that your family be more gentle with their devices!)