Can't open my iPad mini
First of all, I assume that you have enough battery power on the iPadWhen you see the apple icon on your ipad, hold the power- and home button for several seconds. The ipad will turn off and back on again. After this you can release the buttons when the apple logo is visible.

When the ipad is still stuck on the loading screen, you could preform a DFU (device firmware reset)-reset. Do not forget: by preforming a dfu-reset, all data will be deleted from the iPad.

A tutorial on how to enter dfu-mode can be found here
Make sure that the ad is turned on before you start following the tutorial.

To check if you successfully entered dfu- mode:


there should be an iTunes logo with a lightning/30-pins cable on the screen of the ipad
when the device is connected to iTunes, you should get a popup that the device is in restore mode and it has to be restoren before it can be used.