Are you accessing the same AP with either open or WPA2 connections? If you are your Cable router may be limited on how many connections it can allow access though.
I would go to a coffee shop some where which has an open WiFi service and see if it connects that way if it does that points back to your setup as being the issue Vs the iPad.
If you still can't connect on the coffee shop's open WiFi service I would erase the iPad and reload everything. Ouch!