Go look... Premiere Elements Updates http://www.adobe.com/support/downloads/product.jsp?product=40&platform=Windows
But, I doubt you will find any recent updates for PE4... since the current version is PE8
If you have Win7 PRO or above, go to http://www.microsoft.com/windows/virtual-pc/
Otherwise, try the compatibility settings to run PE4 as if you were using WinXp
You were obviously watching the little line of text, during launch. After the OS and the CPU, what was the next line of text? That is likely where the program is having issues. If it goes by too quickly to see, you might want to video the Splash Screen, focusing closely on that line of text, and then rewind and Pause on that last line.
If you have any non-Adobe audio-editing programs, it could possibly be the loading of a VST. This ARTICLE discusses that.
Three more things to think about would be having the very latest video, and audio drivers, plus the latest version of Apple's QuickTime.
There are probably updates and hot-fixes for Win7, but I do not believe that SP-1 has been released yet. If your Windows is set update automatically (the default), you have likely gotten those updates and hot-fixes. Those can often render a video, or audio driver totally obsolete, and prevent PrE from being able to work with them, often causing launch to fail.
Good luck, and hope that something helps,
PS-BTW did PrE 4 ever launch for you, or has it always hung?