Professors can be a great resource. They can help you learn about the field, including problems that bother potential clients (things for you to solve) as well as information on existing competition, They also have relevant resources that can help you find clients or investors.
In fact, they might be exactly what your board of directors needs, assuming they are famous in a relevant field.
Some profs are nicer then others... Some will be glad to help, others might feel they are too busy to be bothered.
Be sure that you have your act together, since they are busy, and if you are not ready, and don't know exactly what you need, you might not get another chance with them.
I am not sure that profs will talk with potential investors on your behalf unless they are really convinced that you are serious enough and know what you are doing. This is not likely to happen unless they are on your board...
In what field is your startup. and what does the professor teach?