I started in a company with some similarities to what you describe and by taking the initiative to learn all the positions I became a great asset and have now excelled into computer network administration.

This does take time and plenty of patience. I would sit down and write out the pros and cons of your specific position and where you would like to go in that company. If you strongly feel that you have no way to excel at that company then I would suggest a change.

If there was talk about promoting you but it has not been done yet, maybe you are too enthusiastic and hardworking for the people that you would be working with after the promotion which would make these "non-contibuting" staff members finally look as bad as they actually are if you know what I mean.