I am using a Nokia 6300 phone, but this walktrough works for most Nokia phones. I recently changed my price plan, and internet access stopped working for Opera Mini and other Java applications - but the built in browser had connection to the internet!
After a lot of fiddling around, I found out that Java applicatons need a separate access point configured in order to work. Here's how to do it:
1) Get your GPRS/internet configuration from your provider. They usually send those out by text message, so that you only have to accept the configuration and save it.
2) Go to menu - settings - configuration - personal configuration settings (in the bottom) - Add new - choose 'access point' - Give your access point a name under 'account name' (optional).
3) Under 'data bearer' make sure it says 'packet data'. Choose 'bearer settings' and now you have to enter the address of your packet data access point. In my case, it is called 'internet.bibob.dk'.
The address is the most important thing to get right.. usually all the other settings are fine if you just use the default. The address of your access point can be obtained from your provider. Usually you can find it on their homepage on the pages telling you how to manually set up the internet connection / GPRS.
Your Opera Mini and your other Java applications should be able to access the internet now through the phone's connection to the internet.
If there is anything, I should clarify or if you have any questions feel free to ask them in the Comments! :o)