It sounds like your phone is not connecting to the cellular provider network, and you are also unable to connect to the Wi-Fi network. I would recommend these troubleshooting steps from the article named:
iPhone: Troubleshooting issues making or receiving calls
Toggle airplane mode: Tap Settings > Enable Airplane Mode, wait five seconds, then turn off airplane mode.
Check your phone settings:
Check your Do Not Disturb settings: Tap Settings > Do Not Disturb.
Check for any blocked phone numbers: Tap Settings > Phone > Blocked.
See if Call Forwarding is turned on: Tap Settings > Phone > Call Forwarding.
Ensure that your software is up to date:
Check for a carrier settings update.
Check for an iOS software update.
Note: Some updates may require a Wi-Fi connection.
If the iPhone has a SIM card, reseat the SIM card.
If the iPhone 4 or iPhone 4s is on the Verizon network, dial *228 from the iPhone and select option 2 to update the Preferred Roaming List (PRL). The PRL determines the cellular towers the phone uses for cellular service, selecting those with the best signal strength.
Reset the network settings: Tap Settings > General > Reset > Reset Network Settings.
Try to make or receive calls in another location.
Attempt to isolate to one network band:
If you're having the issue on LTE, disable LTE, if possible, and try again.
If you're having the issue on 3G/4G, disable 3G/4G, if possible, and try again.
Contact the carrier to check the following:
Your account is properly configured to use the specific iPhone that has the issue.
There are no localized service outages.
Your account doesn't have a billing-related block.
Your calls don't have errors on the carrier system.
Restore the phone as new.
Also, for your Wi-Fi network issues, I would recommend this article named:
iOS: Troubleshooting Wi-Fi networks and connections
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All the very best,