It could be that there is a broken link between the icon and the executable file. You can navigate in Program Manager to:

C:\Program Files\Corel\Corel Graphics 12\Programs and you will find all the .exe files for the Graphics Suite 12. If you can launch the program from here, you can drag out new icons and make desktop shortcuts by dragging copies with the right mouse button and click where you want the shortcut copy to go.

If these programs are not in this folder, something when wrong with your install, it is best not to do a custom install if you are unsure what you are doing.

As with any other program, DRAW likes to install in one spot on the hard drive and if your drive is badly fragmented, it can cause problems. If you also have any version of CorelDRAW open, it usually asks you to close them, it is possible it could interfere with the installation.

Let me know if any of this helps.