I am baffled once again; can malware stay in a computer even with the hard drive replaced?

I have a computer that completely froze up. I had to unplug it to shut it off. This computer never shut off even after many months of just sitting in a corner. Recently I took it to Best Buy to have the hard drive replaced. I have the computer back but it is still stuck " on " as it is plug in and therefore still completely useless. I thought it best to seek advice here at LQ. Can malware completely freeze up a computer even after the hard drive has been replaced? Thanks!