@EA_Shepard Before contacting EA Help Chat the first time a few days ago, I uninstalled ME3, reinstalled it, tried to launch it again, and got the exact same problem as before. Yesterday, I contacted EA via Chat a second time, and they confirmed, like you said, it was not a game wide problem, and it would not be resolved if I just waited a few days.
During the second Chat, I was told to:
1. Open Windows File Explorer and copy/paste this 'url' into the address bar: C:\ProgramData\Electronic Arts\EA Services\License.
2. If you can't copy/paste this 'url', you can enable the "View hidden files and folders in Windows" option via these steps and navigate to the folder manually.
3. In the "License" folder, where you should be if you've followed the above-shared steps, check if you can see a file called "71067.dlf". Please note: the file can have a different number!
4. If it's there, delete this file and launch the game again. The game should now work.
I found the license folder and there were four .dlf files in it, all of which had different numbers than "71067". I deleted the first one, tried to launch ME3, and it failed the same way as before. I deleted the second .dlf file, tried again, and ME3 launched, no problem. This procedure sounds basically the same as the one you recommended, the problem apparently being a bad .dlf license file. The EA rep said that once ME3 loaded, the deleted .dlf file would be regenerated somehow, I assume from information stored with the game on my EA account. Anyway, I didn't go back to check to see if a new .dlf was generated.