guessing malware problem

Hi I could use some help: My mother has a windows 7 laptop, an hp pavilion g6. It is now inoperable: programs, eg windows explorer, internet explorer, anything, do not work past opening if they open at all but the mouse moves freely. the start menu does not open and task manager does not open. opened programs cannot be closed. Being in safe mode with or without networking does not help and the same thing happens.

I have no idea what the problem is. could it be malware? my mum is suspicious of an appearing and disappearing icon in the system tray. the icon looks like some green blocks arranged in a table, rows and columns of green blocks. the computer only shuts down via a long press on the power button.