A probable Fix
Has anyone figured out how to get on Facetime I put in my Apple ID and password, and it says, "check network connection". We have WiFI and I get my mail and on the internet just fine. Can't figure out why Facetime won't accept me.
I got a new ipad 2 yesterday and have had issues exactly as you describe. Apple support guys were unable to help.
I have now fixed this on my Ipad and would be interesting to see if this fixes for you.
Go to Settings, Network, Wifi and select your wifi connection. Go to the settings of it by pressing the blue arrow next to it.
Then in the DNS server list add , 18.104.22.168, 22.214.171.124 to the list.
( The comma is important to add to the existing IP address that you will have in there- the existing address is most likely your ADSL router IP address)
This instantly fixed it for me and worked 1st time after.
If it works for you i will post how i came to this solution.