Any restrictions set up on your iPhone, or is it a managed device?
If you check the settings for Mobile Service, is Mobile data enabled, and can you see details about your carrier in the section below that, for example Network Selection and Mobile Data Network-> Mobile Data -> APN, Username, etc?
If you connect your iPhone to your computer, using the original Apple USB cable, does the computer recognise the iPhone?
If yes, can you reset the iPhone to factory settings and set it up as a new device, without using the latest backup?
This would be a way to rule out a software issue.
Restore your iPhone, iPad, or iPod to factory settings using a computer - Apple Support
If your computer does not recognise your iPhone, you should visit an Authorised Apple Service Provider or Apple Store next to your place and ask them to diagnose your device.
Apple - Find Locations