I have just bought a cellular ipad 3 , on a different site, do I need a sim card?

To use the cellular service, yes.

Here is an iOS troubleshooting articlethat may help. One of the points that seems to help a lot of people is to shut down the router completely, that is, unplug to make sure it is really off. Then startup the router, give it a few minutes to establish the IP address and DHCP, then startup your other components, computers, iPad.

The WiFi+cellular is supposed to work without a sim card on WiFi so the issue is probably the handshake between the router and iPad.