If the computer is still working, the simplest approach would be to install a tool like ProductKey, License Crawler or WinKeyFinder and see if any of them can find your lost license/product key.
Unfortunately, if the solutions above didn't help with your problem, I can find very little information regarding AngioImage on the Internet. All I could find is a product that costs between $11,000 and $16,000, and I'm not sure that that's the one you've lost the license for. However, since we're probably talking about medical equipment, I recommend contacting the suppliers or the manufacturers and seeing if they can help you out.
