Thanks for the detailed info. This seems pretty weird...
My first guess would that it has to do with a multi-monitor setup, which
normally isn't a problem (I use multiple myself, as do many others), but there is the catch that the engine always/only tries to 1) start up on whatever is designated as the primary monitor and 2) use that monitor's current resolution settings. Some kinds of virtual solutions or other strange setups can theoretically interfere with that.
Sounds like you did already test with one monitor though, so maybe it's something else.
In any case, the first step here is to look at the engine run.log or crash.log located in the main directory for each. There may or may not be a crash log, but there'll always be a run log, and we can use that to see exactly where it stopped and possibly why, or at least hopefully make a more accurate guess as to why
So check for those files in REXPaint and Cogmind and share them here so I can maybe see what's up. (That
both don't work at least tells us that yes it's something about the engine not being compatible with some aspect of the environment, but it's also worrying in that REXPaint doesn't even do fullscreen or require anything except a small window at the very least... anyway, we'll see.)
If there is no new run log at all when you try to run it, then the program isn't even starting up, which means the original DLL issue may not have been resolved. In fact, I'm now wondering if you have the latest correct DLLs... Microsoft just this May updated the MSVC2010 DLLs and there's a new download link, and if you used that without the new instructions I added to the DRM-free email just last week, then you may have installed the wrong ones and it only "sorta works but doesn't tell you it's a DLL issue"?
The new README has been updated to the following text:
* If Cogmind complains about DLL files, your system needs the MSVC++ 2010 Redistributable Package (x86), which can be downloaded and installed from here: https://www.microsoft.com/en-us/download/details.aspx?id=26999. After clicking "Download" it will list multiple versions, and the one you need is "vcredist_x86.exe". (Alternatively, the required files can be installed manually by downloading "msvcp100.dll" and "msvcr100.dll" from the web and putting them in your "windows/system32" directory, but the Microsoft installer is a simpler and quicker approach.)
The main thing is there only used to be a single download, but now they've split it into
three, and a lot of people will assume they need x64, when they really need to install x86...
