What happens if you leave Task Manager open, and look at the Disk 0 graph, or the CPU graph (make sure to select the options to "show as logical cores", and "Show kernel times").
I had something similar happen to a system of mine, CPU would stop, Disk 0 would go to 100%. Either Win10 was remotely imaging my disk over the internet (who knows what kind of spying capability that they really have in there), or I had some sort of SATA error, that hung a disk access, and then from that point on, Disk Access for Disk 0 was basically at 100%, because no further requests could go through.
The mouse would move for maybe a few seconds, as would the CPU graph would update a few times, then everything basically hung. No BSOD.
Never solved that problem.
Edit: It wouldn't manifest itself right away, it waited a little while after boot, after the system was running for like 10, maybe 15 minutes. It sounds kind of similar to what you're experiencing.
Edit: That was with Windows 10 (a few versions ago). I see that you edited your post to indicate Win7 Pro. I haven't heard of this problem happening in Win7 (Pro or otherwise), but maybe...?