Received my upgrade phone but phone number is not syncing so I cannot make calls

Sounds like the sim is not activated. 

https://www.att.com/activations/

when I try to activate the SIM, it says it's already activated on my old phone and I've tried taking it out and putting it back in, turning the phone off and on, etc.

when I try to activate the SIM, it says it's already activated on my old phone

Pardon?  The phone that's lost or stolen? That phone should be blacklisted. You should be activating a new SIM card that came with your new phone. 

and I've tried taking it out and putting it back in,

Taking sim out?   So you have a new SIM, but it's not activated. 

turning the phone off and on,

Clearly the new SIM card is not active. Please use the link and follow the instructions to activate the SIM card.

The online activation asks for your Wireless number and your ZIP code and then walks you through the process of activating the SIM card in your new phone.

It may ask for the ICC ID number on the SIM card

Hey there, hellow0rld! Let's get your SIM card active so that you're able to start using your replacement phone right away.

First, make sure that you're following the steps to activate your SIM card as @formerlyknownas advised.

Also, you will want to make sure that your account is current and active. To check your balance info in myAT&T:

• Go to My bill and look in the Make a payment section for your balance and due date. Want details for another account? Select that account from the dropdown.

In fact, you can use our Star Services to get free wireless account updates by text. We’ll send you a text message with your account balance, due date, and more:

• English - Call *BAL# (*225#).
• Spanish - Call *SAL# (*725#).

If your account is inactive then this may explain why you're not able to use your new phone after taking steps to activate your SIM card.

Try this and let us know how it goes. We want you to start using your replacement phone immediately.

Lar, AT&T Community Specialist