Macbook Pro -OS crash + Broken screen

Hi all,

my Macbook Pro has a broken screen. For the last few months I have been using an external monitor as my primary display.

However, I recently ran an update on my operating system on my Macbook whilst connected to the external monitor.

Unfortunately the update crashed my system, requiring me to reinstall the OS from my Time machine back up. However, during the update, the external monitor lost connectivity with the Macbook, requiring me to reconnect the external to the Macbook, so I can have display access to my Macbook, so I can reinstall using Time machine.

Thus, the problem now is that I can not connect the external monitor to the Macbook, so that I can reinstall my Macbook from Time machine.

I am desperately trying to find a solution to the

is egg/chicken scenario/problem.

Please HELP!