My Video card on the PCI Express x16 port on the Gigabyte Z77MX-D3H motherboard blocks the x1 PCI Express slot.
Can I install a PCI Express x1 card (short connector) into a longer PCI Express port (x8/x4)?
Yes you can. You can install any smaller pin PCIe (PCI express) in a larger slot, so in a 16X slot you can put a 16x, 8x, 4x or 1x card in, for an 8x slot you can put in a 8x, 4x or 1x card, 4x can take 4x, 1x and so on. Just make sure that you put the first part of the card on the left side of the key/not in the slot, then the actual pin part on the right side.