Can I sue AT&T for breaking their promises on unlocking?

Two months ago we wanted to switch our phone carrier because AT&T was not suiting us. We called AT&T and they said if we paid the termination fee they will unlock our phone. We paid off the termination fee which was a little over $1200 plus the last bill. We had to wait 1 month for the bill to actually be received from AT&T. And, I have requested multiple times for AT&T to unlock my iphone 5. And, today after 1 month from the time when AT&T received the money from the bill, it is still not unlocked. And, I obviously had to buy another phone because I didn't have one during all that time. I even called AT&T's customer service and they didn't even recognize the phone's IMEI attached any of the line at all. But, my final question is if I can sue AT&T for all the damages that they have done and for breaking their own contract and agreement.

Added (1). Also, I'm tired of corporation thinking that they can push their customers around just for capital. I want to teach a company like AT

Go ahead and sue and you will teach AT&T a big lesson.

After being with ATT for over 10 years and never once that I was late on my monthly payments. I have the same issue today 12-9-14. I paid 1900 dollars for ETF on 5 phones and att promised to unlock my phones after I paid ETF. All phones got unlock except for the account holder's phone. I too will find a lawyer to sue them.