Which is more important - Interconnects or PCs?

Well, I'd say power cords.

Because without them none of your gear would power up.

All are equally important, in my experience. Just wait until one doesn't perform as desired, and see how easy it is to ignore.

Too shay gunbei

All seriousness aside, I too think that it's difficult to organize a hierarchy of cables because it's so system and environment dependent.

If you have dirty AC, power cables might yield the best gains. If not, speaker cables or interconnects might do more. Also, it depends on what cables in the chain you're replacing with what, and then you have how each component might react to the cable.

So confusing.