Wifi troubles: Connection time out with fios and wep password

What security on that wireless router are you using?

 

Change the encryption to WPA/WPA2 personal.

Try without a password on the router and see if the Mac Mini can connect. If not try from the installation disc - Could have an issue with the airport card.
If it can then its obviously just the encryption

 

May be unrelated, but my MBP started doing that today: droppped out, then while it could see my network it gave a "connection timeout" whenever I tried to connect. I fixed it by killing the "Airport Base Station Agent" process. The base station agent was restarted automatically and then I could connect fine.

There's no deep knowledge of the OS behind this - it was just a hunch that I decided to test before restarting the machine (and which saved me a restart). My idea was just that some piece of network software was misbehaving, and since all a restart would do is restart it then if I could guess which bit and restart it myself that might fix the problem.