I suppose you are going to ask me for a picture right?
Always helps.

And being able to identify the monitors always helps narrow down common problems on certain models.
But it sounds like either a bad power plug connection on the ones coming up blank or needing a slight tweak for the sync on the ones coming up scrambled.
Could just be monitors needing the general refreshing they tend to need after 20+ years. (cold solder joints, capacitors, adjustment, etc)
When they come up "blank"...... do you hear any high voltage static when you first turn it on?