The biggest problem is running a quality video signal from a remote location. Is the rack near your computer? If so, it is just a matter of getting a standard, full height rackmount case. The rest is just like building any other computer.
As luck would have it, there is one on shell shocker on newegg this very hour: http://www.newegg.com/Special/ShellShocker.aspx?cm_sp=ShellShocker-_-11-147-155-_-10122012_5
You can also just get a 19" rack shelf and set a normal case/computer on it. http://www.ebay.com/sch/i.html?_trksid=p5197.m570.l1313&_nkw=19%22+rackmount+shelf&_sacat=0&_from=R40