I have a Linksys wireless router and find that I have to restart it (pull power, wait a few seconds and plug it back in) fairly frequently because I get behavior like you're describing with both my iPhone and iPad 2. Before going to crazy with other fixes I would restart your wireless router and restart your iPad 2. Then if it still doesn't work you'll need some other trouble shooting steps.
Some of the more obvious things to check;
1) Does the wireless router have Mac Address filtering turned on, if yes is your iPad 2 permitted to join
2) Do other devices connect to this wireless with no problems?
3) Any chance the password didn't get typed in correctly?
Someone would have turned on MAC Address Filtering since it is off by default.
To see if it is on log into your router with your PC, click on Wireless on the upper set of menus, then click on MAC Address Filter and see if is Enabled. If it is Enabled add your iPad's WiFi address from settings->General->About to the list.
If it is not Enabled you could try changing the Wireless Channel on the wireless Basic settings. If you have any other WiFi devices that are on the default channel (6) you might possibly have some interference issues.
One last thing, have you successfully connected this iPad to any WiFi networks? If not try another network & if that doesn't work either make a Genius appointment and get it looked at by apple.