Answer

If the contract with the original company forbids this, and you signed it when you were hired there, then it seems to me that you do not have permission to violate it (unless you get permission from your current company). If you can interpret the commitment as applying only to another company and not to a venture, then fine. Especially since you say you will try to make sure the main job is not affected, which implies that it's not trivial that it won't be affected.
I don't think it makes a difference whether you get paid for it or not. I assume they are not bothered by the extra money you'll make; the reason they had you sign this was only so that your mind would be free for the work you do for them.
Shabbat shalom,
Michi