My SIM seems to have died. What now?

I have an AT&T / ZTE MF279 with an old unlimited AT&T data plan that has been working fine for quite a while. Yesterday it went on the fritz. A friend has the same device and data plan, and he brought it by to use for a while until I get mine fixed.

I did some testing and swapped the SIMs and my device works fine with his SIM in it, and his device does the same weird stuff mine did with MY SIM in it. So I'm guessing something happened to the SIM.

What should I do now? Can I activate another sim and attach it to the existing account? Or do I need to activate a new SIM and set up a new data account?