Do you have the right dataplan on the phones?
It is a BESAdmin rite of passage to go through the gauntlet of correcting the right BES data plan with your carrier.
Under Manage Connections on the device (OS 5 and higher), there's a services status which tells if connected to the data network.
For BES dataplan testing.
Want to check if a device is provisioned correctly?
Sign up for free to the BlackBerry Expert Support Center. https://www.blackberry.com/besc/dashboard/
Then use the Enterprise Activation Readiness tool.
All at absolutely no cost to you or your organization!
The BESC gives you a suite of valuable tools, and includes a Complimentary Support Incident should you need to contact BlackBerry Technical Support directly.