3G Iphone not connecting to internet?

My daughter uses our old 3G iphone as an ipod around the house. Suddenly today she could not longer access the internet using it… We've done hard reset and factory reset. Still it's not connecting.
Any ideas?

Added (1). I guess I should clarify, it's connecting to the Wi-Fi, it's unable to access the internet once it's connected.

1) Does the iPhone show Wi-Fi connections? Yes
2) Correct password? Yes, connects with no issue just doesn't access the internet.
3) Go to general settings and go to reset and reset network settings. *check* didn't work.
4) Mobile data - It's not used as a phone anymore. Has been used as an ipod for the past 2 years (or thereabouts) and suddenly today wasn't accessing the internet.
5) Updated the software, still no luck.
6) did a full restore and still nothing. Any other ideas.

Does the iPhone show Wi-Fi connections? If yes then have you made sure that you are entering the correct password. Try uppercase, some are password sensitive (i'm sure you know) if no, go to general settings and go to reset and reset network settings. If that does not work, go to general settings go to mobile data and make sure that is on. Then make sure that the software is up to date on iTunes. If that also does not work then try a restore and when you turn it on set up using Wi-Fi and try and connect to Wi-Fi that way.

what happens when you go on safari and go on google for example?

Try turning off, wait 10 seconds, and turning on your Internet router.
Try going to another Internet location (Example: Starbucks)
Take to Apple Store.