Q: I bought a new Mac Mini and tried to pair my keyboard with the Mac Mini. They will not pair via Bluetooth. What is wrong?

You have 90 days of free AppleCare telephone support, I'd suggest calling them today. You can also troubleshoot using Apple's bluetooth troubleshooting guide.

http://support.apple.com/kb/ts3048

Try:

Troubleshooting wireless mouse and keyboard issues

try this method:

You need at least a USB mouse. If you don't get any option to pair a keyboard, click through the setup until you get to the "Create Your Computer Account" screen, right click in any of the text fields and select Substitutions --> Show Substitutions.  From there click on text preferences.  The preferences pane will popup and from there you can just click the back button (next to show all) to get to the full preferences menu.  Next click on keyboard, then select setup bluetooth keyboard and you're golden.