I find crunchbase, owler, linkedin etc overpriced, and they don't really have that great data especially on emerging startups - there's few hard data points they have, and some bias towards companies who volunteer their data (or investors who do).
If you can narrow down your focus, you can manually download some stuff from crunchbase etc for free.
If that's not enough, it's a good exercise to scrape them. It's not trivial as they are trying to prevent scraping with quite sophisticated techniques. But, since you are a CS major, I think you can figure out ways around it, especially if you are careful and not greedy trying to make copies of everything they have very quickly.
I also think there is some value in looking at the edgar database, I believe some filings are for privately held companies (such as Form D ?)
Anyway, do tell if you find better answers!