Franniehhk the behavior you are currently experiencing is fully expected when trying to restore from a Time Machine backup. To attempt to recover from this action you can try running the uninstallers located in Applications/Utilities/Adobe Installers followed by using the CS Cleaner tool. From your original post it appears you have already done this however.
This leaves one last option. Format, reinstall your OS, and then restore only your documents and settings from the Time Machine back up. You should then be able to install the software successfully from your installation files.
Adobe Creative applications are not designed to be copied from one computer to another which is basically what the Time Machine restore is doing. This is why the applications are not behaving properly on your new Macintosh.