We do this all the time at work, it's probably an electrical thing. Remove the DVI computer from the problem and get the monitor working with just the display port converter, then try to add the working DVI system into the mix. Getting both to work independently will give you a baseline that will help you find your problem more easily.
Two other pieces of advice--
1) You might just try VNC on one of the computers instead, it actually makes it much easier to do things like copy and paste between computers and the screen sharing issue goes away as do the multiple input devices (which become annoying)
2) There is a free program called Synergy out there that EVERYONE who runs multiple side-by-side computers should at least know about--allows you to easily share keyboard and mouse (although it is really made for multiple monitors so it may not be for you, but still you should know about it, it's fantastic)
Have you ruled out the DP converter not working? I'm currently switching a monitor between VGA and DVI-D the same way so it should be possible. More details on your video card, the specific cable and monitors would be useful as well – Journeyman Geek – 2012-05-28T11:52:22.230