f3 and f4 media key stopped working...

There's a couple of things:

1. Apple Menu -> System Preferences -> Keyboard
2. Untick "Use All F1, F2, etc keys as standard keys"
3. Click "Keyboard Shortcuts"
4. Click "Restore Defaults"

F3 and F4 on my mac are for the Dashboard and Mission Control.

What are these keys supposed to be doing?

On my mac the media keys (play, volume up/down, mute) are further to the right (F6,7,8,9 perhaps-not at my mac at the moment).

If you are indeed talking about media keys they changed a bit in High Sierra. They control not just iTunes but also QT Player and Safari.

On the rare occasions where they did not appear to work I found that they can be activated by first starting playback with a button or the space bar.

You could also try resetting SMC

You could try rebooting in safe mode to see if the problem exists there. Then try a normal boot.