Apple ID Verification Failure

I recently was sent a new phone through my warranty. I signed out of my old phone and factory reset it. I backed up it to my Mac before hand. I successfully restored the new iPhone 7 and inserted my SIM card. However, I CANNOT get into my iCloud to change anything. It will ask me to sign in over and over again. I enter my information and it says “Verification Failed - There was an error connecting to the server”. It won’t let me do anything! Sign out, change information, reset and erase data. Nothing! I tried removing the device from my account to re try. I reset all network settings. I’ve been trying to fix this issue for hours now. No luck. Please help.