Old HD in running in an external case should allow copying of all data files to their new home.
Installed applications will need to be installed again from scratch because previous installation has integrated with the operating system as part of getting them to run.
There is one small group of self executing files which can be transferred, usually a freebie to run some specific task, but often better to download the latest and start fresh.
Eventually when all is smooth you could wipe the old drive and use it as a store for data.
Also useful if you want somewhere to keep restorable images of drive C: using 'Acronis'
This will avoid having to scrap everything if your OS gives trouble again, but that is another story.