Is there a way to completely remove all data access, including WiFi, on iPhone 4? We want to give our teen a phone for talk and text only. She has to earn trust again before having access to anything online. We are upgrading and would like to hand down one of our old phones. Our plan is through Sprint if that makes a difference.
All iOS devices come with built-in "Restrictions" settings as a form of Parental Control. By enabling Restrictions, you can restrict access to certain functionality of the device, including web browsing and other capabilities.

To enable Restrictions:


Open "Settings"
Navigate to and tap "General"
Scroll down and tap "Restrictions"
Tap "Enable Restrictions" and enter a passcode. Make sure this is a passcode that only you and your partner will know. It will be used to deactivate restrictions once she has earned your trust, or to temporarily enable certain functionality.
Toggle off any functionality that you do not want your daughter to have access to (and toggle it back on if you want to incrementally allow her access again)
Browse through the extra settings and decide which you wish to restrict access to (Facebook and Twitter can come in useful here).
When you are done, simply tap out or close "Settings"


While this isn't a perfect solution, you will be able to prevent her from browsing the web, using FaceTime or installing any apps this way until she has redeemed herself. 

To further restrict her, you can do as @Buscar has suggested above and contact Sprint to limit her cellular data access, and I would recommend either changing your WiFi password to something she can't guess (and thus input to connect when you aren't looking) or, even better, block the iPhone's MAC address from your WiFi router. You can find the MAC address in "Settings" -> "General" -> "About".

Doing all of the above will essentially limit her to simply phone calls and texts (she will be access any media such as music or photos loaded on to the device, however).