i've just come across a similar issue when trying to help configure a friends home system. his existing wireless devices had internet, but his new ipod Touch didnt, even though it logged onto his wireless system.
the issue was a combination of having too many wireless devices all arguing with the router for connection space, and the router was old. Try a complete factory re-set of the router. failing that, try assigning static IP addresses to individual devices, failing that, buy a new more up to date router.
it's not your ipad, its your router which is the issue