The fonts that are going screwy are the Articulate fonts. I did have a Google font I was using, but it was fine after I realized that I needed to install that font on the new computer.
After posting this, I found an older thread where the person appears to have had a similar problem to mine, and one of the solutions that they gave her was to delete the Articulate fonts and then repair Storyline by reinstalling. I've gotten as far as deleting the fonts, but then I realized that I didn't have the product key, since the laptop was sent to me with it installed, so I've been waiting to get that information and continuing to edit on my current machine while holding my breath that it doesn't crash.
I'm curious about why my file has problems when other people aren't having any. Maybe they aren't using the Articulate fonts.