iPhone 4 has 3G connectivity but can't access internet
Settings -> General -> VPN (should be not connected, if this is a personal device)
Settings -> General -> Cellular -> Cellular Data (turn off, reset the device) 
After the device boot-up 
Settings -> General -> Cellular -> Cellular Data (turn on, reset the device) 


IF that doesn't help (follow this )


Settings -> General -> Reset -> Reset Network Settings (this will delete all Wi-Fi passwords) 
Settings -> General -> Safari -> Clear History -> Clear History
Settings -> General -> Safari -> Clear Cookies and Data -> Clear Cookies and Data
Settings -> General -> Safari -> Advanced -> Website Data -> Remove All Website Data -> Remove Now (** All data saved in Safari will be deleted)
Reset the  device