Client blackout on startup

Last 2 weeks i randomly got this problem, now i have reinstalled 4 times and troubleshooted + hextech repair and the whole circus.

It works again after i restart the computer, but then the client (and gameplay) laggy and below 10 fps, i usually have 60+

I have reinstalled graphicdrivers and rollback, still no apparent sollution.

This is my last hope, this problem is soon to be the reason i quit playing League.