iPhone 3GS works fine using WiFi but using 3G only Mail works, not any web apps

[bjoymarsh]

I live in Australia and have a 5 year old unlocked iphone 3GS, using Vodafone network, and problem has started only since I returned from time in the US where I used an AT&T SIM. No 3G was working at first; after many hours with Vodafone support, doing many different resets, and eventually totally backing up and restoring phone via iTunes, still no luck, so then (on my own initiative when all they offered was to return the phone for repair or get a new one), I used unlockit.co.nz to change the APN to live.vodafone.com, and now Mail (my default, Yahoo mail only, but not Gmail) works fine but no other websites/gmail/safari etc return any results - but wifi works perfectly, and if I put the SIM in another compatible smartphone, 3G does work. I am on IOS6.1.3.

I have turned the phone off, reset network, re-run unlockit, taken Sim out and replaced it . Any ideas? Please??