Well since the data works when the SIM is in another phone, we know it is a problem with the device itself. Here is few things we need to check.
Do you have the right plan? If you device is an Apple device, you have to have an Apple data plan. For Android phone you need to be on an Android plan.
Did you buy the device form AT&T? If you bought the device form another carrier even if it’s unlocked, we do guarantee all features such as data will work. One thing which is important is you have the right APN settings in your device. iOS devices update theses settings automatically. For Android devices you will find instructions for programing the APN’s here.
Last thing to try is master reset the device. It is important to back up your device before doing this. For instructions visit our Device How to Page and select the Make and Model of your device.
Thank you for being part of the Community Forums, and have a great weekend.
Anthony, AT&T Community Specialist
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*I am an AT&T employee, and the postings on this site are my own and don't necessarily represent AT&T's position, strategies or opinions.