I suspect that you are correct and it's related to the had disk. If the Gnome shell is having trouble accessing data from the drive then it could easily cause the system to become unresponsive over time.

When it happens you could open a shell and run top to check the iowait metric. It's on a line like this:

%Cpu(s): 0.1 us, 0.0 sy, 0.0 ni, 99.8 id, 0.0 wa, 0.0 hi, 0.0 si, 0.0 st

The value in front of wa indicates how much time the CPU is waiting for IO. Unless you're in the process of copying large files it around it should be low. If it's high then that points to the disk.

You could also install the systat package and check with the iostat tool

$ iostat 1 10

This will print disk IO stats every 1 second for 10 seconds. The output will provide metrics for each disk in the system. The first line is an average, you can get just that by running iostat with no args or iostat 1 1

If you want to kick gnome back in to life then you could try pressing ALT + F2 and then r follwed by return. If that doesn't work then killall -HUP gnome-shell should do the trick.