/sci/ - Science & Math

A pretty big company, were I'd like to do my internship, is doing an online event to show what it's like to work there. After a presentation they'll let the participants ask questions to some employees, talk with managers, and form small teams to try to tackle a typical real-life problem at the company.
The event is posted as a job/internship opening, and a CV and a cover letter are required. My question is: what do I write in the cover letter?
Since it's just an online event, wouldn't it be out of place to include the usual sappy paragraph about why I like the company so much, why I am a good fit (for what even? this is just an online event), and so on?

Also, reading cover letter examples online, it seems that nobody is shy of openly complimenting themselves, but I very much dislike it. Should I do it anyway? And what if I'm just mediocre in certain areas, do I outright lie?