Does it have a DVI plug? Looks kinda like a VGA but rectangular. There are adapters for HDMI to DVI. Cheapest thing to do would be to replace that old monitor! Prices are really down these days. Replace it with a 32" LCD TV for about $230 lately!
DVI does support HDCP so that would be a valid option.....additionally, like idr said, cheapest thing would be to probably replace the monitor.....I did find a company out of Taiwan that makes a pretty snazzy product that seems to be just what you would need but it ain't cheap...seems to range for $300 to $500 for the various devices....
even if not interested in the device, their web site is pretty informative and actually fairly interesting reading for those who might be interested.http://www.hdfury.com/
Note: As I mentioned earlier, I suspected any company marketing such a device would face legal action and my suspicions seem justified as the HDfury products are no longer available in U.S. stores....of course the manufacturer is located in Taiwan and they claim that they would be perfectly happy to sell you one regardless of where you live....which may or may not get you a visit from the postal inspector