Difficult to say without knowing what machine and what OS version we are talking about here. However, you should not only download the latest OS updates, but also all available Firmware updates for that machine and install them. Not all firmware patches are distributed through Software Update, so you should go to apple.com and search the support and downloads section.
If this computer is still in the warranty or has Apple Care: Don't waste your own time on it, but take it to a service center.
If this computer is still in the warranty or has Apple Care: Don't waste your own time on it, but take it to a service center.