While electronics may survive a single blast with "accidental" shielding, the problem is many items would have been subjected to dozens, even hundreds of EMP bursts. By surviving the first EMP burst, the owners may have been lulled into a false sense of security and fail to properly prepare for following bursts.
So yes, it's probable some survived due to being shielded, or just plain blind luck, but it would seem much of the necessary infrastructure will take a while to rebuild. In the meantime, I'm with James - elements still exist, but service will be patchy at best and subject to frequent outages for days, weeks, even months at a time.
...at least until somebody noticed they can't find their favourite porn sites anymore and the Nigerians can't find any gullible idiots to scam.