Below is a Quora question I once answered with the title of this post being the question asked. The answer below is unedited and just as answered
Any! Why constrain yourself by thinking a mechanical engineer can only start a few kinds of startups? Some of the best startup stories in the past 10–15 years came from people who were not mechanical engineers or even formally trained (i.e. credentials) for the kind of startups they started.
If anything, due to the systems thinking and methodologies which mechanical engineers are trained in, they can begin startups which deal with almost any problem.