I have been working with the ios developers, engineers for quite sometime now, since November to be exact. I had the same problem as most people on here. It all started out with a "searching" for signal in the status bar. This was an iphone 4 with ios 6xx. I tried everything I know, airplane mode back and forth, reset network settings, and so on. After a restore in DFU mode, I had no "searching" for service and the phone was working again. I then put ios 7 on and it was all good. Had no problems with 7.0.1 either. When 7.0.2 came out I upgraded....now the phone was stuck with 2% left of the process and returned a error code 3. I tried and tried everything to get it working, but was getting stuck on the same last 2% of the update. I then started to look at the logs. Baseband issue. ok, so I went to my cell carrier for a fix. Was told to go to Apple. So I went to apple hoping for an answer....which I did not get. The genius actually told me "you developers are smarter then we are" and I have never seen this error before. GREAT I said...they wanted 200$ for a replacement since it was out of warranty. I left the store. I called Applecare. I explained to the representive that I had a huge problem and so does a few thousand other people. I told her everything, then next was speaking to an ios software analyst. From there the rest is history, Apple sent me a "Capture Data" program and I was able to recreate the error 3 while the capture data program running. This intern was sent to Apple over a secured link and they had the info they needed. My idevice was out of warranty, but they did send me a BRAND NEW idevice and not a refurb. I still continue to talk with my "guys" there and send them any info I can for this matter. It way be fixed in 7.1 update but one really does not know. Just keep trying and be nice. And if you have registered any Apple products they will see that, and let them know you have spent a lot money on Apple products..as they saw all mine and said "Wow you own like everything we have made!"
Good luck and please report back.....have you tried kennethyoungs freezer trick yet? It wont hurt one bit if your idevice is out of warranty.