Using Cinema Display with a desktop PC
Since you have DisplayPort on the PC, and MiniDisplayPort on the monitor, this should be a snap. Assuming that the monitor's Mini DisplayPort cable is detachable, just get a MiniDisplayPort to DisplayPort cable like the ones shown on this page:
I don't think the mDP cable from a Cinema Display is detachable. On my 20" Cinema display the DVI cable is not detachable. So, one would need a this cable
plus this adaptor
Or if you can find it, a DP(male) to mDP(female) adaptor/cable.