"The liberal professors are the villains."

Nailed that one.

She, clearly, was correct. Why didn't her argument for laissez-faire capitalism become the dominant politico-philosophical force in America that it should have been?
Why did Marx win out?

"The universities are the real villains in the picture."

BOOM! Mic drop.

She's right as far as she goes, but needs to talk about regulation.

Regulation of business -- any line of business -- is sold as protecting the public, but that's a lie. Always. The real purpose of regulation is to drive small, and especially new, competitors out of that line of business and keep them out, thus reserving the field to a small number of giant firms. This process does not have to go all the way to one firm -- a literal monopoly -- to enable the abusive behavior that defines what most of us call monopoly.

For instance, there are hundreds of banks. But banking is so over-regulated that it's impractical for new banks to arise, and they wouldn't be allowed to have better policies about, say, privacy or overdraft fees than the existing banks. That's effectively a monopoly. And until the public sees regulation for what it is and demands its abolition, it will stay that way, and we will have fewer and fewer choices.

Greed and the desire for the incompetent to rule by brute force

Aren’t patents and copyrights tools of the government that interfere with free markets?

I will say that there is one critical aspect that is supported by Rand which does give a monopoly and it is not government-supported: that of the copyright, trademark, or patent. Musicians are probably the quintessential example of this: an entire industry made of monopolists! If you're a Shakira fan, you can't get Shakira music by listening to Elton John. Same with Wierd Al and Taylor Swift (although because Wierd Al does parody you could argue that you're getting the tune but with different lyrics). After musicians you would have the motion picture industry. No one can do a remake of "Casablanca" without getting permission from the original producers.

Let's also not forget that Rand, herself, lauded the monopoly of a good idea protected from intellectual theft when she invented Rearden Metal in AS - not to mention Galt's atmospheric generators!

Dead on. All the power to control comes from the government. All big companies enjoying monopolistic power or a phantom version of it (e.g. Google) do so with government support.

Minimize government, and big companies automatically lose power, or are producing value.