iPhone Activation with NO SERVICE problem My iPhone7 started with "NO SERVICE" problem, I fix it by restore system but a week later the problems appears again.
Then I do a fabric reset but now I can't activate my Iphone because it can't read data from SIM. 

My SIM works good in an old model (iPhone4). When I try activation by iTunes, there is only a white screen with the word iPhone and no activation buttom or something. 

How can I activate my phone to restore my old backup?

PS. I can't take it to Apple because there is no Sellers on my country.
It sounds like you have a physical problem with your iPhone; specifically the SIM card slot.  It could be a broken connection within the slot itself or a problem with  the circuitry.  The fact that the SIM works fine in another phone eliminates it as a potential problem

In order to activate your phone, you need to be connected to your carrier’s network.  This means you need a valid SIM.  Since your phone can’t read the SIM, it can’t connect.  Unfortunately, there’s no DIY fix for this.  Apple or an authorized service center will replace the phone’s logic board; there are some repair shops that might be able to do board level repair.

Until you get that fixed, you can’t activate it.