You can use a start boot cd, search for OPHCRACK, it can remove your password or decrypt it. Or you can try Hirens Boot, there is a loot of tools to remove passwords
If suddenly shut down is high temperature or electrical problem. If it was your gpu, pc would stay powered on even if screen turn black or something like this.
I had removed the battery and left the macbook without charger about 3 days. today, i replaced my battery and my macbook become to charge and power on.
My macbook is programmed to start 6am and shutdown 11pm. after a day, it doesnt start. $65 here is 28% of minimal salary, I dont want a free diagnostic, i want a fair price. I'm from Brazil.