I agree that would be the easiest and simplest solution if you have a recent copy of the jre folder somewhere. (Of course, that's assuming it's not a problem of the silly Windows Installer, InstallShield, and chances are it is not InstallShield).
Me, I finally threw in the towel, and scoured my registry file to delete every reference to the jre6 folder, the Users/[WindowsAccountName]/AppData/LocalLow/Sun/Java folder (I have Win7), and any subkeys to all versions of Java. Before that, I made sure I had a backup of the registry file by exporting the entire file to a ".reg" file. Also, I was very careful to avoid deleting any reference made within other programs' registry keys like Adobe Photoshop and such. A very tedious and time-consuming task (for safety sake, regedit does not allow you to delete more than one reference/regkey at a time).
BTW, if you ever need to install both the 32bit and 64bit versions (and this need has been addressed by Sun-Java in regards to using both a 32bit-only program and a 64bit-only program that require Java--like Internet Explorer), make sure you put the 32bit Java and the 64bit Java in separate folders. In Windows 7, I believe that Java 6 would normally install the 32bit in the "Program Files (x86)" folder, and the 64bit in the "Program Files" folder.
I also believe the version of the Control Panel Java module is dictated by which version of Java you installed last, which is only important for the auto-update feature (I suspect that the module still controls both 32bit and 64bit versions for everything else). I find that whenever you open a webpage that uses advance Java, a Java icon pops up in your system tray (the one with the clock). When I have 32/64bit Javas in separate folders, the Java Control Panel listed in the icon submenu is the version associated with the Java used in the webpage.