MacBook Pro screen broken and was using 2nd monitor fine until I started the process of turning FileVault on
Things to try in your situation include:


switch your external display on first, followed by switching on the MacBook Pro (within a second or two) - hopefully it'll get the signal it needs to display the MBP's output
if the above doesn't work, and assuming you only have the one user account, then switch on your MBP and wait long enough for it to be at the login screen. Then press the return key once and carefully type your password followed by the return key.
if you have two or more user accounts you'll need to use your keyboard to select the one you want to login with. You can do this by pressing the first letter of the username on your keyboard (assuming each account starts with a different letter), followed by pressing the return key once and carefully typing your password followed by the return key. 


If none of the above work, please let me know and we'll see what else we can try.