This is why I thought you'd just want access to the data (that, in some cases you might have to prepare for), after making a fresh install and getting it working nicely already.
The SSD install neither knows nor cares (for the most part!) that 'installations' exist on the old drive. It's just all data, of various kinds, so long as you don't try to invoke the runnability of any exectable item that now sits there. It's like if you copy any Program Files (or whatever the location) items on the SSD into the My Documents on it, where it would be (almost[1]) as disassociated, and the original (SSD) install would still work nicely enough.
Uninstallers generally tell the current OS (the one on the SSD) how to remove currently installed things (that were installed on the SSD), by doing such things as removing resource files, reverting registry changes, undoing associations, deleting links to things that no longer exist.
If the SSD's system has never
had these changes made, I'd actually presume that trying to run the old drive's uninstallers would immediately go "Oh, can't do that... can't do that... can't even work out how to do that..." and either suggest that it's already removed or pretend that it got rid of everything or possible tell you point-blank that it's wrong. I'm not sure why it might have reset your desktop (well, I have some ideas, but it assumes that installers/uninstallers do things that I'm not sure why they'd every do in any sane situation... which probably perfectly describes some hack/work-around situation that some (un)installers have to use for reasons dictated mainly by MS's intentional obfuscations).
But I'd suggest you just don't even try to do that. Pick up savefiles, dabble into (human-)readable config files, etc, and use this information (perhaps!) to rejig the fresh installation (of any application, itself upon the fresh installation of OS). And your old-HDD "My Pictures"/etc data can be copied across to SDD "My Pictures" at leisure... or establish a new root directory structure on old-HDD to gradually sort and shuffle things as you work out what you actually want to keep.
Then you're free to just delete all the unwanted (even system-level) directories on old-HDD. With care that you're not deleting something new-OS now thinks is part of it. Everything under "\Program Files" (or "\Program Files (x86)") can probably eventually be removed once you've checked there's nothing you actually want out of each subdir. The (hidden) "\ProgramData" directory might have some gems of usefulness in it (or under "\Documents and Settings", I forget when Windows changed their nomenclature), but it's the one currently on C: that counts (which you don't even access by explicit C:/...whatever), not the one on D: or whatever letter it is. Delving into the "\Users" structure you'll probably find (eventually!) your masses of saved MP3s, JPGs, .DOCs, etc that you might have accumulated and previously expected to see under the Documents, Pictures or media-themed areas of your designated usespace.
Possibly if you haven't actually done anything drastic, your old drive could be removed from your new computer and replaced back into the old computer to allow it to boot up (and without stopping your new one from doing so) if you still need to find out how to access the data that you think you are missing. That's if you haven't donated even more parts between the system. At this stage, though, I'll admit that I'm purely guessing as to how much fiddling you did that I would not even have thought you would. If you don't have to reverse the process, and it still works well, then I'm not going to pursuade you to try anyway.
Oh, and the caveat that I'm fairly good with the system layouts of any version of Windows version prior to 8[2]
[1] By dint of the correct drivers/etc still existing in the correct directories, you could probably still run
some of the cross-copied executables, but once you uninstall the main-install (or, possibly, get an update) there'll probably be confusion by the copy-executable (not changed) finding that .dlls that it might previously have picked up now being missing/changed.
[2] I could tell you about the time that I used the DOS6.2 version of DEFRAG upon my brand new Win95 machine, because I still prefered the DOS interface. Except that DOS6.2 didn't have any concept of the LFN data and wiped, so ending up with directories such as "C:/PROGRA~1/MICROS~1/..." and "C:/PROGRA~1/MICROS~2/..." was the
least of my problems... And forced me to learn the ins and outs of the system quite quickly