I also had come with this error 1651 when I first connected my new iPad to iTunes and it was there ever since.
Every solution found on Apple forum and tested on my system was useless. The AppleCare expert contacted, after a long trial and error phone session, believed it was a hardware problem. Even the proposed solution from Apple at discussions.apple.com—2762611 was useless to me because I already have the most recent version of iTunes.
Oui mais voilà!
Today, I once again connected my iPad to iTunes and, surprise!, iTunes was asking to install a new version of iOS on my iPad instead of displaying the same error message. I authorized downloading and installing of update 4.3.4(8K2). The procedure went on perfectly well and the error message 1651 appeared again after the installation!
My conclusion is that this error message is, well..., an error, to be ignored, since it does not prevent iTunes from searching and installing updates correctly.
Maybe the problem is different for some users but in my case, this is it.
Oh! by the way, the sim card has nothing to do with it. I don't have one either.