Yeah, the problem with character selection is because the specified ROM version is meant for a dedicated 4-player cabinet. The game is looking at 4 different coin-in switches, one each dedicated to the 4 playable characters. Therefore you will always be forced to be Leo if you coin up using the P1 coin button, for example.
Since this game was available as a conversion kit back then, and because not all donor cabinets would have 4 players, they also released a ROM that is compatible with 2-player cabinets. It allows you to use any coin button to credit up, and then select which turtle you want to use. I think TMNT2PO is the 2-player ROM.
Using the 2-player ROM would probably be preferable for most of us due to the convenience factor, but there is a workaround for the 4-player ROM. You just need to re-map the controls so that they become associated with the turtle you want to use. For example, if you are using an XBOX360 controller and want to be Donatello, re-map the controls so that Player 3 is your controller, and coin up by pressing ‘3’ rather than ‘1’. Or, if you like to map the coin button to something on your controller, map Player 3 credit to that button. Of course, you’ll have to repeat this procedure every time you want to play as a different character.