Did it install and you're just getting errors trying to run it? If so, try clicking on your Start button. Then, go to All Programs, find the entry for Adobe Photoshop Elements 4 and "right click" on it. Select Properties, and in the Properties dialogue click the Compatibility Tab and try running it in XP Compatibility mode and see if it works that way.
If not, then it is really not compatible. Just buy the latest (Photoshop Elelments 9) while they offer $40 mail-in rebate (Ends January 5, 2011)