If the WIFI is working, and the cellular data is not working I would probably approach my carrier and get them to do an account refresh, and put in a new sim card. It would make sense if you can use the phone, the data would work also.
I'm not saying this is a fix, but it's one of a series of things that can be done for free, that are not in the replace or fix hardware realm and are simple.
I've also gone the replace hardware route under Apple Care when it turned out that the problem was truly some error on their part that couldn't be resolved.
The last time however, they replaced the hardware because they could not figure out the problem, and when I got it home and restored it the problem was still there!
It took quite a while til I could isolate the issue and come up with my own fix. The Google searches turned up just a couple of people with the same problem and no one had figured it out.
The point is simply to get it back to a known good point.
Software can be prone to x in a million bugs that they generally catch, but we also live in a world where various strings of data can also lock up software and cause it to fail that they don't catch simply because it is so unexpected.
If that fills up past the wrong spot, it can affect other parts by overwriting what is supposed to be there.
I have no idea about the 4 years of text's and I can't imagine why that would be a problem but then again that might exceed what was expected by a developer, so that might be worth exploring.
The device firmware update did not nuke my texts. I do back stuff up to iCloud and my computer and before I updated to 6 I had completely rebuilt the phone software from backup first to get rid of any cruft just to be safe.
I have gone through carrier provisioning problems when upgrading to new hardware, and they assigned things wrong, requiring going back and re-setting them so I would check with them to see if they are registering your device correctly.