I think you should had a comment for "Main Font Replacement" advising to use it only with an english localization. I play in French and when I tried this mod there were no support for non english characters, so there were blank instead of the correct characters.
It surprised me too. But it really happened. I had the same same symptoms as OP. Clicking on "Run" would make MO blink and then nothing. Reading the log file there was a line for each time I clicked on "Run" that meant plugins prevented programs from running (I don't remember the text sorry). So I did what I explained and, miracle, I could run programs through MO. Or I didn't understand OP and am completly H.S., in this case sorry.
I had a probleme where MO 1.2.2 wouldn't run anything (not even Skyrim), I found out it was the bsaExtractor plugins that prevented this. So I moved Mod OrganizerpluginsbsaExtractor.dll out of the directory to disable it. After doing that, I could launch what I wanted from MO