I also tried to run Mathcad 14 under Windows 8 or 8.1 when I got a new machine last year, with the same results. The program is actually running, if you check Task Manager it shows that it is running and using about 20% CPU but nothing is displayed on the screen. No display or indication that it is running. I have to manually shut it down with Task Manager to free up the CPU for other applications. I also tried running it in all the different compatibility modes. No better luck.
Never have found a solution to the problem.
Since I have used Mathcad since version 3, I started working backward to see if any of the earlier versions would work. I got back to Mathcad 8 Professional and it will work with Windows 8.1. I don't think PTC owned them back then.
I'm retired now and only use it recreationally so it not a problem. Never did find an upgrade path to PTC Prime 3 that I could afford now that I don't use it professionally. They don't seem to have an affordable full function individual Home version like Mathematica does.