Trying to find display replacement for iMac.

iMac Intel 27 EMC 2429 Repair Model A1312 Mid 2011 2.7 3.1 GHz Core i5 or 3.4 GHz Core i7 Processor

I'm trying to find a display for a late 2011 27 inch iMac, but it's hard to find the right parts for a reasonable price. I was wondering if the 2009 27 inch (or any older model same size) would work with the 2011 version. I found a few, reasonably-price, 2009 displays, but there's no point in buying it if it doesn't work for the 2011 system.

Another question, I attempted to hook the iMac up to my HDTV to get that to work. There was no display on the HDTV. I used a miniDV to HDMI cable and was under the impression that it would just work. Is this a bigger issue I should be thinking about, or something inconsequential?