It is very unlikely it is related to the hard drive, the motherboard is a prime suspect, as will as the cooling system. depending on the spec's unless it is a powerful system with dual GPU's the Video is built into the motherboard, if there is any damage to the board you could get the issue you are showing. My first instinct i s that it is possibly related to cooling specifically the Video section of the board, if the cooling fan is failing intermittantly the core temps will rise and that kind of display will happen. The fact that it is still showing the mouse pointer indicates it is not a full video card failure but rather a rendering problem, which are very oftenn caused by heat. I have seen this on several of the Dells at work, the last one had pluged fins in the main heat sink and the fan could not cool it properly, I cleaned out the heat sink and the thing works like new.
Heat can also cause slightly damaged traces to fail off and on when the temp expands various parts the ability of some traces to conduct signals can degrade so you might want to look into a utility to log the temp sensors on the system, if it is heat related you can check the logs for the temps the next time the screen goes nuts and if it is spiking that is you problem.