Mac mini won´t boot up
It sounds like the hard disk may have been damaged, or perhaps its connector has become disconnected.

If you can dismantle it, try disconnecting the hard disk and reconnecting it. If that makes no difference, then it sounds like you need a new hard disk (or even an SSD).

Installing is possible from a USB stick, so you don't need to use the DVD drive. But while you are dismantling the machine, you might want to look at getting the CD out of the drive!

Also - you didn't mention which model/year the Mac Mini is. That makes quite a difference to any instructions someone might want to show you.