Hi I have iPad that has little shattered screen and one corner destroyed with few lose pieces. What I would like to do is...

So I got one of these machines for free, I plug in mouse, keyboard and monitor. I turn it on and screen would be dark, fan...

Did you check that DC adapter has same polarization than the original, did you check that adapter works? If yes and yes, and it didn’t work. You have code FUBAR.

Did you try to load in safe mode? If it doesn’t work you need another mac to create bootable USB and instal it it from there. I think data will not be affected. If nothing else work you will have to install it clean. You shouldn’t perform hard restart, but use terminal “sudo shutdown -r now” command.