Q: turn off the display but prevent sleep

Yes there is.

You can use the command Ctrl + Shift + Eject which just puts the display to sleep but the Mac will carry on running. I do this quite often so I added a hot corner to put the display to sleep. This is in System Preferences > Desktop and Screen Saver > Screen Saver > Hot Corners and then you can just choose the corner and select Put display to sleep or any other commands.

Hope this helps!

Oh sorry! In that case, I think going to Energy Saver in System Preferences and changing computer sleep to never should do it.

Have you tried the energy saving setting that controls the hard drive sleep, and set it to Never?

Then it won't matter the minutes display is set to wait until sleep, so long as it's not also never.

If there is a problem with this not working, you may check into an SMC reset; or perhaps also

the NVRAM/PRAM, as one or both may be in control over some aspect of this (dys)function.

•Intel-based Macs: Resetting the System Management Controller (SMC)

•About NVRAM and PRAM

There may be other issues with the later versions Mavericks energy saver selections; in the

older systems the matter was refined and less a problem. Your mileage may vary.

Good luck & happy computing!

edited 2x

Should those third-party applications to modify sleep appear to not

help the situation, you may have to remove them totally since they

can also work against the normal function of system preferences.

Modifications can cause grief. Sometimes Console (utility) logs can

show by date/time the actions in the system & help point to a cause.

Hopefully you can resolve the issue satisfactorily.

Good luck & happy computing!

This seems to be my problem! When i switch the display off by the hit the action corner, the my mac goes to sleep after some while, no matter that i use some 3th party app to prevent it!

check this out.

http://osxdaily.com/2011/09/14/disable-the-internal-screen-on-a-macbook-pro-or-a ir-in-mac-os-x-10-7-lion/

I wanted to turn off the display while connected to an external monitor and the lid is open. what I did was not exactly the same but the code might help.

shutting the monitor is very annoying as the existing information on the web I believe gets outdated with each new release. some people suggest using a magnet to trick the computer

Apple should definitely do sth about this 

Apple doesn’t routinely monitor the discussions. These are mostly user to user discussions.

Send Apple feedback. They won't answer, but at least will know there is a problem or a suggestion for improvement. If enough people send feedback, it may get the problem/suggested change solved sooner.

Feedback

Great, many thanks. I will try. Im new. turned to mac from pc after using iphone for many years. Macs are good generally but funny in some ways. E.g. this site asked me to enter a verification code that was sent to the same computer while i was trying to sign in:) 

You can install Amphetamine  to prevent your mac sleep.

https://itunes.apple.com/us/app/amphetamine/id937984704?mt=12