Exactly what the title says, and no other output. This is happening on Gentoo. What should I try to do to fix it?

Would that command not be 'boincscr'?

Your right, my bad, the title is wrong, I'm running the command "boincscr" like you suggested

boincscr is expecting the data directory to be in /var/lib/boinc. If it's not you need use -boinc_dir command line parameter.

Just checked and /var/lib/boinc definitely exists, and to my knowledge, I haven't changed it to use somewhere else, so that shouldn't be the issue.

Wrong permissions will also cause the file or directory to "not be found".
But if you haven't changed anything, it's probably not that either.

Have you ever used the screen saver before?

Sorry for not being able to respond for a little while, not on my current Linux install, no.
When I used to run boinc about a year ago I would use the screensaver with xscreensaver. From what I remember I had issues with that as well, but I could at least run boincscr and it would show things. I'm pretty sure that was also on a different distro I think (I was using Arch then, now I'm using Gentoo).

Actually, I just tried running it again and now it manages to at least open up a window! Now it just says "screensaver loading" and the screen is black. I didn't make any changes that would affect boinc, so I'm not sure why it's (at least partially) working now.

A net search shows a lot of results, including this one on SETI from 2 years ago:
Linux Mint 18.1 stuck on "screensaver loading"