I just found a way to get rid of those annoying company logo animations that play every time when you start the game.

Just go to Doom 64 game files, find a folder named “Movies” and delete all the movie files inside. Enjoy.

I know I'm 2 months late.

Ehh there's a better alternative than deleting video files that could (possibly) affect the game in some way (hardcoded filenames for example):

Open the console on DOOM 64 by pressing Tilde (~) and type the next command: g_showintromovie 0
What this does is disable the intro movies (except the cool intro firefight) and doesn't change anything aside from that, it doesn't even affect achievements (via Beth.net)!

But Midway? What if we can't?
You totally can enter the console on the PC versions (Console versions are stuck with the movies), maybe you have a different keyboard layout, maybe you fucked up and unbinded the Tilde, or maybe you think the console is really complex (It isn't!).

Thanks!

I restored the movie files I had deleted, then I tried your command in the console, and it works.

Your method is definitely better as it doesn't involve deleting any files, although my method works equally well and hasn't caused any problems with the game. Still, your method is better.