Intermittent gray screen instead of login screen at start

I've looked at OS X Yosemite: If you see a gray screen at startup, which implies it could be a firmware issue (since I don't see any symbols or the Apple logo). But I can't find any Early 2011 firmware that lets me install it. Anything I try says it isn't compatible with my system, which to me implies I already have it installed.

I will start the system, it will load as usual, and then it gets stuck on the gray screen that normally briefly appears before the login screen. In the past, I was able to see verbose output even here with Cmd-V, and it would be stuck on some NFS server thing. However, Cmd-V doesn't show what's happening anymore, so I'm not sure if it's still the same issue.

The fan is often active while it's stuck like this, implying that it's doing something. I just wish I knew what it was doing.

This issue is intermittent. If I continue to use Ctrl-Cmd-Power to restart the system, eventually it will reach the login screen. I have to do this between one and (approximately) 10-12 times for it to work. Normally, it's 3-4 times.

Things I have tried:

- Unplugging peripherals (except external monitor, because the internal display is busted).

- Reinstalling OS X.

- Safe boot (holding shift).

- Internet Recovery (but it didn't work; I would hold Option-D, it would start loading it, and then it would give up and just restart the system. no clue why)

I'm guessing it's some kind of race condition or something, but I'm not really sure.