I've read my manual about the PCI_E slots, and it says I should use the PCI Express 16x_1 slot (shown as #1 in the picture below), but my heatsink is blocking that slot. I was wondering if it makes a difference if I choose to put it in the PCI Express 16x_2 slot (shown as #2 in the picture below). It should be the same thing, no? Do I need to change a setting in BIOS if that's the case?
Are you certain that's the way the heatsink needs to be oriented? Even with the really big honking heatsinks, they usually make it so that there's one way to align it so it doesn't interfere with the PCIe slots. It's a fairly standard amount of space they have to work with. Almost all the pictures I see have it installed like this:
So I'd try aligning it horizontally if there's room. If there's not ... well, do you really need a heatsink that big? Really, unless there's some reason why your setup should have extra trouble dissipating heat, you'll do just fine with even a mid-level CPU cooler like these: