Safe Mode does a number of different things. Hold shift at startup, but have your userid and password at the ready.
A parade of unusual things happens.
• Your Mac loads just enough of the kernel to do a disk check. Then it proceeds to do a disk check. This can take an extra about five minutes.
• your userid and password are required, even if you normally auto-login. So have them handy.
• Your Mac adds ONLY a minimal set of Apple-Only extensions, Not including graphics acceleration extensions. Screen updates will therefore be wonky and slow, and the screen may re-draw multiple times, but it ultimately should be accurate.
• Your Mac assumes defaults for as many settings as possible. This is the key for re-setting the screen, but there is a little more to it: Resolution is likely to be lower and settings ordinary. Use this as a starting point to customize settings to your liking.
Any changes you make in Safe Mode will "stick" in regular mode after you restart.
• after restart in normal mode, your Mac sill take slightly longer to start up [once] because it rebuilds some system caches.
"Works in Safe mode, fails in regular mode" implies "It's something you added".