start up with black screen

These 2011 MacBook Pros (17” and 15”) have known GPU defects that will cause various issues such as no display, artifacts, blank grey screen after Apple logo and lines on the screen. In order to fix this, you will either need to find somebody who can solder a new GPU, or find somebody who will do the DeMux mod (such as this send-in: https://doslabelectronics.com/Demux) in order to disable it and use Intel HD 3000. Since it’s a 17” it still has quite a bit of value, so if you go the DeMux route I wouldn’t worry too much about putting in more money than its worth, plus with this method you can use dosdude1’s Catalina Patcher or OpenCore Legacy Patcher to run Catalina or Big Sur.