How can I find the owner of an obstinate iPhone?
Your best bet is to just place an ad on Craigslist and in the paper in the lost and found sections. If someone tries to claim the phone, have them identify the picture on the lock screen.
I used to work at an Apple Store Genius Bar. We were not allowed to give out any information from our system ever. If you're located in the US and the phone has a SIM, it probably has AT&T as a carrier. They will not be able to give you any info on the phone either.
Just to provide some insight as far as why Apple can't help you contact the whoever might be listed in their system, remember that a computer or iPhone is a transferrable device. We would frequently have customers bring in a device for repair that was purchased secondhand and the original owner's information was still in our system.
Let's say Tommy buys a MacBook Pro and registers it. Later, Tommy sells his MacBook Pro to Kate because he's broke. Kate purchases the MacBook Pro but does not update the registration. A month later, she leaves the computer in an airport and you find it. You take it to the Apple store and they say, "Oh, here is all of Tommy's info. We'll just call up Tommy and he can come get his MacBook back."
Tommy is not a very scrupulous person, and he fails to mention that he sold the MacBook Pro a month ago. He comes and picks it up and now he has Kate's money and his old computer back. Sweet deal, right? So you can see why this isn't something that Apple would be willing to do.
The Apple employee you talked to was not trying to be obstructive when he wouldn't help you out, but there's a lot of liability things at stake here. They were pretty committed to the idea of protecting customer data, sometimes to the point of idiocy when I worked there, so they're pretty much a dead end as far as returning the phone.
I'm not sure why you can't just press the "OK" button under the No SIM message.
If there's no passcode go into > Settings > General > About you can view the phone's IMEI.
If the owner has reported it missing to the police they should be able to reference the IMEI (their cell carrier should hold that info if the owner doesn't have it themselves.)
So far I'm guessing you haven't contacted the police, I'd recommend you turn it into the police station nearest the location your parents found it.
You can use this page on Apples website to find out what version the phone is, and what carrier it was using if you are in the US due to verizion and ADT using separate cellular networks.
You could then hand it into to the network provider.
Failing that you should hand it in to the nearest police station to where it was found.