Is it on the screen or the housing?

If it is on the screen is it glass, or plastic?

A CRT monitor screen would be easy to clean with alcohol.

It's on the screen itself which is a type of plastic. I did try alcohol and that didn't do it.
Someone suggested the magic eraser, and another suggested nail polish?? I'm being cautious about what I try because it is our computer monitor we are talking about....don't want to do further damage.
Thanks.

This sounds like one of those situations where you want to go Googling and determine if the manufactures of the marker and the monitor have any suggestions. They will want all model numbers and that sort of thing.

No nail polish remover as it could mar, as could the Magic Eraser. Try hair spray--the type of alcohol in it melts some inks and I have had it work on some markers too.

Your success in getting the ink off the screen is partially determined by the ingredients of the magic marker. Here is a website for four different products - all slightly different. One of them should solve your problem. :)

Here is a link that might be useful: Monitor cleaners

I don't want to sound like a "Negative Nancy", but I have had permanent marker on one our monitor screens for about 3 years now. I have repeatedly tried to remove it, but nothing has worked....it has faded over the years though from repeated attempts, but the marks are still there. (lesson learned though, ever since then I have made sure to keep permanent markers out of the hands of my daughter!)

Good luck!

Rubbing alcohol did the trick on the monitor...thanks everyone.

Phew, the only thing I could think of on a LCD would be white-out and I think that might still leave less than desirable results! I am glad it is removed because I figured it would be pretty permanent on a LCD monitor. The old CRT's were easy to clean almost anything off of. These new ones are a different story.