Let's say you have a relatively modern game like Shogun 2. The loading screens take several minutes. This bothers you and you'd like to improve it.

What is actually going on when loading screens are up? I'm guessing assets are being loaded into memory from disk, and possibly being decompressed first. However, what is actually causing the slow down? The memory? Mainboard? CPU? HDD?

If you had $100 to spend on upgrades and your only goal is to speed up loading screens without reducing other performance, what component of the computer does it make sense to upgrade for maximum benefit? If your answer is "it depends on the existing setup", what sort of benchmarks would you run to determine what is causing the bottleneck? What if you had $500 instead?

I give the two budgets for context. I am not asking for actual recommendations about which component to buy (nor are the numbers supposed to be rigid limits), but what features are important when shopping for components with small and large budgets (a large budget could allow buying multiple components which are not so good on their own, but work particularly well together).

I mention Shogun 2 as an example, but I'm asking about reducing overall loading times, across all games, not just one game. Therefore, "put it on a solid state disk" probably won't be good solution, because putting every game on your SDD will quickly fill it up.