You can also try holding down the left side Ctrl+Al+Shift buttons as you launch the program.
When this has happened to me in the past, it's because a Windows Update knocked something out of whack. An uninstall/reinstall (with a reboot in between) usually fixes it.
And you can try posting to the Photoshop Elements forum. They may have some ideas.
With the understanding that your issue is with Premiere Elements 3, have you seen the Adobe TechNote for troubleshooting Installation and StartUp issues for Premiere Elements 3?
"Repair" has never worked for me with these Premiere Elements versions. The clean uninstall/re-install route is the route.
If I were experiencing this problem, I would first take the advice given earlier in your thread, namely, going for a System Restore.
That said, I would suggest that you use the systematic Adobe's troubleshooting approach for this issue as cited in the link.
Please let us know how that works out.
I got the correction to PrE, thanks.
Now, when the splash screen comes up, there is a little line of text that shows the components that are loading. It goes by quickly, and is not that large to begin with. Can you see what the last component, that it tries to load is? I've found that using a video camera to shoot the splash screen helps, as you can pause the camera in playback to see just what that componet is. This might give you a clue.
If you have added any audio editing programs, it is likely that a VST from it is causing the hang. PrE will attempt to load all VST's (these will usually be .dll files), and can work with most. Others it cannot work with, and you'll usually get a message telling you that it cannot work with this one, the first time that PrE launches after one is installed. These do not affect PrE, but you will not be able to use that/those VST(s). Now, some do cause problems and at launch. These will crash PrE, or PrPro, and the only hint is that little line of text on the splash screen.
Another bit of trouble shooting that might yield clues as to what is crashing PrE will be the info in this ARTICLE.