A clone is a clone and must be used as such. And changing the driveletter certainly isn't "as such".
If you want a working bootable system on the e:-drive, you INSTALL it to the e:-drive, and not CLONE it to the e:-drive. Then install all applications (Program Files and such) also to that drive.
If you prefer to edit the registry yourself, go ahead. I would export it, change "c:" to "e:" using a text editor, import it again and see what happens. An interesting experiment.
I'm going to keep it simple and describe my hard drives as containing one partition each. That's not how my drives are set up, but the real setup is more complicated and irrelevant.
I just installed a new drive. That makes for a total of three drives, giving me C:, D: and E:. I cloned C: to E: and edited boot.ini to add the option to boot off of E:.
It boots from E: flawlessly, but since the cloning procedure didn't change the apps' properties to reflect their new location, they're all still executed from C:. As my goal is to eventually remove the apps from C:, I need to change their properties to refer to E:. Do I have to perform this tedious task manually, or is there some automated process that can acomplish this?