Q: My iPad shows that I am connected to wifi but safari tells me it cannot open the page because I am not connected.

So, this is happening at places like Starbucks, or at home?  If at places like Starbucks, you usually have to access the sign in page to connect. 

You are detecting the wifi, but not connected to it.

Look at iOS Troubleshooting Wi-Fi networks and connections  http://support.apple.com/kb/TS1398

iPad: Issues connecting to Wi-Fi networks  http://support.apple.com/kb/ts3304

iOS: Recommended settings for Wi-Fi routers and access points  http://support.apple.com/kb/HT4199

Additional things to try.

Try this first. Turn Off your iPad. Then turn Off (disconnect power cord) the wireless router & then back On. Now boot your iPad. Hopefully it will see the WiFi.

Go to Settings>Wi-Fi and turn Off. Then while at Settings>Wi-Fi, turn back On and chose a Network.

Change the channel on your wireless router. Instructions at http://macintoshhowto.com/advanced/how-to-get-a-good-range-on-your-wireless-netw ork.html

Another thing to try - Go into your router security settings and change from WEP to WPA with AES.

How to Quickly Fix iPad 3 Wi-Fi Reception Problems

http://osxdaily.com/2012/03/21/fix-new-ipad-3-wi-fi-reception-problems/

If none of the above suggestions work, look at this link.

iPad Wi-Fi Problems: Comprehensive List of Fixes

http://appletoolbox.com/2010/04/ipad-wi-fi-problems-comprehensive-list-of-fixes/

Fix iPad Wifi Connection and Signal Issues  http://www.youtube.com/watch?v=uwWtIG5jUxE

Unable to Connect After iOS Update - saw this solution on another post.

https://discussions.apple.com/thread/4010130?tstart=60

Note - When troubleshooting wifi connection problems, don't hold your iPad by hand. There have been a few reports that holding the iPad by hand, seems to attenuate the wifi signal.

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If any of the above solutions work, please post back what solved your problem. It will help others with the same problem.

 Cheers, Tom

Thank you Tom.  Your first suggestion worked perfectly!  Do you know if this is a systemic problem or is it possibly in my building [old small building..lots of wifi connects]?