Re: How do I pick up messages when my phone isn't working?
No, there is not. If the device is not readable, you will simply not be able to read those messages. If you are able to swap your SIM into another phone, you will be able to read any subsequent messages, but not any already sent to you.
You can log into your AT&T account online and find out who the senders are (if you cannot view that on the screen), but that's about it.