You could have a damaged LCD caused by the various drops/impacts that caused the screen to crack. Ina a worse case scenario, you may also have a logic board issue. However, the only way to tell is to try some known-good parts to eliminate some variables.
You can try to troubleshoot this yourself by looking at these [[Topic:iPad Mini 2 Wi-Fi|guides]] however to test components, you will have to buy them. If your budget is tight, it may be more cost effective to have this looked at by a reputable repair shop.