I had a similar issue 5 days ago. I used to get stuck with a black screen just after the SA client loads and before SA:MP loads (connecting).
My FPS was being unusually high (160+ with highest settings), so I re-installed SA and SA:MP but it still wouldn't work so I just used a program and limited my FPS and it worked fine. Maybe you should try limiting your FPS and see if it works.
I can't really be sure that the high FPS was causing it to happen but that's the only conclusion I could draw after trying various things.
My FPS was being unusually high (160+ with highest settings), so I re-installed SA and SA:MP but it still wouldn't work so I just used a program and limited my FPS and it worked fine. Maybe you should try limiting your FPS and see if it works.
I can't really be sure that the high FPS was causing it to happen but that's the only conclusion I could draw after trying various things.