Aim a flashlight into the screen at a sharp angle see if you can see the faint image of the desktop icons. If you do you know the backlight circuit needs repair. But, from the sounds of it, a freezing screen more often implies the GPU has died.
It might be wise here to look at getting a newer used system Vs trying to replace the logic board. You should still be able to access the HD in Target Disk Mode to then migrate your dads stuff over to the new system if it comes down to that. Or, take the drive out and use a SATA to USB adapter (powered). to hookup to the new system.