This game has regional differences.
Are there any built-in passwords? The system for checking passwords seems to be confusing... unless the passwords just dump game state
Screen mode $28 jumps out of ROM...
Translated Network Play Menus
CyberBall was the only Genesis game with Mega Modem network play to be released outside Japan. Sega of America had planned from the start to release the Mega Modem in America as the "TeleGenesis Modem", but this never happened and the Mega Modem remained exclusive to Japan. All regions, however, used the same CyberBall ROM, which means that the Mega Modem functionality is fully translated; it's just that the "Modem" option on the main menu is removed if the console is not Japanese.
Be sure your emulator is set to either US or Europe (if it has an Asia setting, the game will treat it as a Japanese console). Activate these codes, then deactivate them when the screen starts flashing.
Are there more modem screens?
The FFF660:0040 does not seem to boot into the telephone screen straight away on the Japanese/Asian region settings; resetting will take you to it. I wonder why...