open the laptop, disconnect the battery cable.
plug in the ac adapter and run it without the battery connected. Do you still get blue screen and lag?
Since you already took the battery out, it's not the charging circuit issue.
When you boot up at the ROG logo, do you see the spinning dot circle?
if it were me, I would move everything to a second partition, and then clean install Windows 10 again on the primary partition.
You could first try uninstalling the gpu drivers completely, including deleting the driver. That would help rule out gpu driver issue.