My thoughts...

It's not the disk drives, BIOS or software.
The symptom of the problem gradually worsening and for awhile recovering after power off for awhile points toward a component gradually failing.
With just the boot drive in place does it spin up when power is applied?
If not perhaps the power supply is failing since the disks are good.
In the BIOS does it show any info for the disk: manufacturer, size, etc?
A next step would be to boot from an HP diagnostics CD/DVD and see what it showed.

Now here is something you might try...
Put the laptop in the refrigerator for about 15 minutes then take it out and quickly power on and see what happens.