It's been so many years now since I tried opening this again, and it won't load. It's in the task manager, it's using 25% or so of my CPU, but it will not show up, not even in my system tray. I don't think I'm doing anything wrong here.
If you could please provide some more information to help diagnose your experience.

I doubt this computer has an extremely old copy of BYOND installed. But are you making sure to use the newest installer?

Are you using the beta, by chance?

What OS and version are you using?
Just wanted to point out there isn't currently a beta version. 514.1568 is the current stable build.
Thanks for the replies, I tried restarting my computer and it started working.