I'm trying to use my Apple Thunderbolt display for my PC. If you could tell me what I need to do to make this happen, that would be great.
My PC: http://pcpartpicker.com/p/KFXnVn
To clarify, I need something that I can plug a Mini-DVI and HDMI cable into that will connect my graphics card to my thunderbolt display.
I believe Thunderbolt uses the exact same connector as mini-DisplayPort, so, as long as it is powered separately (i.e. isn't powered by the thunderbolt connector), you should be able to get use mini-DisplayPort to HDMI cable.
That's not going to happen on that build. The TB Display relies on an active PCI-e connection to function. If you had a cinema display this would be possible.
If you want this to work you're going to have to rebuild a good bit of your PC.