I'm sorry you are having issues connecting to the internet through your 3G network.
It appears from the error message that the issue is with your Carrier. See below:
When activating 3G service on an iOS device using a custom Access Point Name (APN), the error message "Could not activate cellular data network: PDP authentication failure" may appear.
Below are troubleshooting steps you can try on your own before seeing the Genius tomorrow:
This article will help you troubleshoot the following cellular data issues on your iPhone:
- No connection over cellular network, but works over Wi-Fi
Follow the instructions below for assistance with troubleshooting cellular data issues on your iPhone. After performing each step, please test to see if the issue is resolved.
- Toggle airplane mode: Tap Settings, turn airplane mode on, wait three seconds, and then turn off again.
- Restart your iPhone.
- Ensure that your software is up to date:
- Remove the SIM Card and reinsert it. Allow the iPhone to acquire the network again.
- If your SIM card has SIM PIN enabled, try toggling it off: Tap Settings > Phone > SIM PIN.
- Try another location. If a different location works, but the original location still does not, contact your carrier to report the issue.
- Reset network settings: Tap Settings > General > Reset > Reset Network Settings.
- Restore the iPhone as new.
- Contact your carrier to:
- Verify that the iPhone is properly set up on the account with the appropriate, current data plan.
- Verify that there are no account-related blocks.
- Find out if there are specific error messages in the carrier logs that could help determine why the issue is occurring.
I hope you are back on track soon!