If you have an old HDD lying around somewhere, try plugging that in for a while. Just load up windows on it and some basic essentials - a browser for example - and see if the problem is fixed. If it is, you know what you need to replace. It could also be the cable as you initially thought, though I usually hear about HDD failing before the cable does.
As for the repair vs replace argument, aside from the BSOD, are you happy with the computers performance? Does it do what it needs to? If so, then I wouldn't bother upgrading anything more than what you need to fix it. Some people seem far too upgrade happy,
needing the latest line of processors or graphics card. Believe it or not, you don't need a quad core processor and GTX670 to run an internet browser. That said, the fact that it uses an IDE cable and not a SATA... well that's probably an indicator for an upgrade

Jeez, haven't seen an IDE cable for years... Can you still get HDDs that use IDE?