I am sorry you are having problems but let me help you.
Based on your description I would not say it is the graphics driver because it is still failing on Safe Mode. Safe mode uses only the necessary drivers from the Operating System to run the applications so the Intel® HD Graphics should not be loaded on this instance.
Due to this fact, I recommend you contacting the Computer Manufacture since a hardware component can be affecting the performance of the entire system.
From our side, You can try reinstalling the driver that can be downloaded here:
If you get a notification message during the installation, it indicates that your computer manufacturer does not allow the installation of generic Intel video drives. You are required to install drivers from your computer manufacturer.
You may try to force the installation of Intel generic drivers by performing manual procedure, see here for instructions:
Here is the zip version of the video driver: