Hi Dave,
Sorry for the late response, I have done some research on this product and found out that a lot of people are having the same issues that you're having.
The "Not registered on network" message indicates that the sim card did not register on the tab 2. Since the sim cards were ok and active, I am also thinking that it has something to do with the firmware of the tab or a hardware issue. Have you tried updating the tab through KIES?
Having checked online without any solutions for this issue, I went to a shop myself and tested a Samsung Galaxy Tab 2 and inserted a sim card, It didn't register although my Galaxy S3 detects it. I tried going through the Settings > Mobile Networks. Since I wasn't able to access Mobile Networks removed and reseated the Sim card (pushed it in and it clicked as if locking the simcard to position) turned the tab On and was able to get a coverage after a minute or two. Asked some technicians experienced on working with Samsung mobile devices about hearing any sim card issues and the answer I got was most people returning the device got a sim card stuck in the SD card slot or a bricked device because of an attempt to root it.
I was about to confirm this as a known issue but somehow it worked on my end, leaving me thinking that there is a problem with your tab. For an attempt to resolve this, try to connect the tab to KIES and see if it needs to update any firmware. If it is updated, just do reset the device just an attempt to fix it. A lot of online resources say they haven't resolved this by factory reset but I still suggest you try this including checking the firmware. Just make sure backing the data first on your computer before any resets.
I hope the information given helps. Let me know what happens then so we could check on what needs to be done if it doesn't work. I'm sorry again you're having this issue on your new Galaxy tab 2.
Regards,
Abe