Try this. Here is a tutorial on using jQuery to get content from a Remote URL.
You can send the JavaScript on the clients end to an IP Address Reporting Service.
You can find one here that is intended for automation.
Perhaps you could modify the JavaScript to take the information and "write" a hidden form element with the IP address.
There is a small chance of errors, etc, depending on security settings of the browser. But if you NEED the IP address, this is what you can do.
Otherwise, if they are on windows, you can put the following info into a .BAT file:
@echo OFF
ipconfig
pause
This will open the window and wait for them to press a key so they can note their IP address.