Thank you for the very quick replies!
bugunner - We verified that the 8-pin CPU power, 24-pin Mobo power, and 6-pin PCI-Express power are all in. RAM is also certainly seated properly in the correct slot. We also verified that the jumper cables for the case are all in the proper position (although there's no real way to test it since all of the buttons are unresponsive).
Calvin7 - As for the graphics, we read that on the box and that is our next attempted fix. However, we removed the card completely from the computer and tried. Upon plugging it in we got the same series of LED blinks and then nothing.