This same thing happened to me, and i had to figure it all out myself, but i think i can help you out. In my case, my level was corrupted, and it was the default level, so i was not even able to open the editor, like you. What i did was:
1.cloned my project in the UE4 Launcher ( by right clicking on the project and selecting clone ).
2.went back to the original project in the launcher, right clicked and selected show in folder/finder.
3.copyed all the files in the project
4.went to the clone of the project and opened it in folder/finder (once again by right clicking on the project)
5.deleted all the files from the cloned project
6.pasted all the files from the original project
I did this so I would not accidentally mess up anything from the original project ( that would really suck ).
7.Then i removed each of the folders ( Binaries, Build, Config, Content, DerivedDataCache, Intermediate, and Saved ), one by one. Each time i removed a folder ( don’t delete the folders, just put them on your desktop ) i tried to open the project from the Launcher.
8.finaly it opened when i had removed the content folder, so i put the content folder back into my project and started removing each of the folders inside of it until i found that the problem was in my default map.
9.then i just removed that, and my project opened fine. Of course one of my level was not there but that was sure better than losing all my work.
Hope this helps!