Open System Preferences, go to Network, Select Airport on the left side, and verify that the first drop down is set to
Using DHCP. Secondly ensure you’re connecting to the proper access point. What are the odds you’re accidentally on a neighbor’s network? If both those conditions are true, you should see a bunch of numbers there (192.168.x.x, 255.255.255.0, 192.168.x.1, etc).
For future reference, simply telling us a problem exists isn’t going to get you answers. Give us some more information: What kind of router do you have? Have you tried plugging the Mini directly in via a cable, just as a sanity check? Is the mini surrounded by a metal desk that may be clouding its ability to connect reliably, but your iPad which isn’t so enshrined is about to connect from almost the same spot flawlessly? There are thousands of conditions that could be preventing this from working, but chances are its something painfully simple. We just need more information to help.