The feature of my car that requires my clutch to be depressed before it will allow me to start the vehicle seems to be buzzing more and more. To test it I pushed the clutch all the way to the floor and turned the key, it buzzed first but then started.
(my clutch is not worn out or anything like that, if that matters)
What might be the problem? and How would I go about fixing it?

It has a new battery, the starter is strong but this feature I am afraid is going to leave me stranded somewhere. Recommendations please?

Thank you
Edit: My problem is caused by a clutch safety switch, I think. I found a Youtube video on it. Please let me know if it is maybe something else.