Thanks to everyone who has contributed to this thread, especially @kennethyoung 🙂.
I just encountered this "unknown error 3" for the first time only a few days ago. After spending hours on this issue, I realized that this is a pretty widespread and unresolved issue. Here's my story: I was trying to update my iPhone 5 (never jailbroken) from 7.0.6 to the latest 7.1.2 through iTunes on a PC because I didn't have enough space to update directly on my phone. Unfortunately, the update process failed and I got stuck in Recovery mode. At first, I was able to exit the Recovery mode using a third party tool. However, I noticed that my phone could no longer find a cellular network. The network status remained to be "Searching..." on the top-left corner no matter what I tried. (I even tried my SIM card on a different phone and it worked fine.) Also, I noticed that the baseband info in Setting was gone/empty.
So I decided to do a Restore hoping that it would fix the issue. Now I wish I didn't. Obviously, the Restore process failed and I got stuck in Recovery mode---for real---this time. I tried a few third party tools and none could get me out of it.
I tried Restore several times and kept getting "unknown error 3" at the end. I have tried on 2 PCs, turning off antivirus program and firewall, unplugging all unnecessary USB cables, etc. Finally, I tried kennethyoung's freezer method, twice. For some reason, It failed when I tried it for the first time. However, I decided to try it again the next day and surprisingly it worked! I guess I didn't freeze it long enough when I tried it for the first time, even though I left it in the freezer for nearly an hour I believe. I wrapped the phone in a paper towel and put it in a sandwich/freezer bag filled with some rice, both times.
Unfortunately, now I face another obstacle which has already been mentioned in this thread. I'm stuck at Hello welcome set up screen because I could *neither get my phone activated through iTunes *nor Wi-Fi. I also noticed that no IMEI info could be displayed when I press the little "i" in a circle thing at the bottom-right corner of the Hello screen. Now I'm not sure if I could ever get this phone activated...
Any suggestions on how to pass or bypass the activation process..? Thanks again!