Try lauching Elements by using the PhotoshopElementsEditor.exe file located your Adobe Photoshop elements programs folder. Assuming it works, you can right click the exe then create a new shortcut from the exe file. You can do the same thing with the PhotoshopElementsOrganizer.exe.
If I remember correctly, making a shortcut from the PhotoshopElementsEditor.exe circumvents the welcome screen.
If you want that welcome screen, you can insert your disc and reinstall. It won't hurt anything or change any preferences other than bringing back the shortcut and changing some file associations. (You know the old every image wants to open with Elements deal.)
If attempting to launch Photoshop Elements from the PhotoshopElementsEditor.exe did not work, reset the application preference file. Corrupt preference files are not fixed by uninstall/reinstall as they are stored outside of the application's program folder. Press and hold in the ctrl + shift + alt keys when you launch the Editor. Keep holding in these three keys until a dialog comes up saying something like "Delete Photoshop Elements settings file." You can release the three keys when the dialog comes up. Press "OK" to accept. Elements should load...