Developments - actually all of your work in Lightroom - is stored in the Catalog.
Only if you have set the option to additionally store to XMP sidecar files, and only then, developments and stuff is stored to the picture folder.
You need to get the catalog from your old PC - search for an *.lrcat file.
Ok, I just found the "Lightroom 5 Catalog.lrcat" file and double clicked it and after LR6 started again it seems like everything is ok. Didn't loose 5 years of developing pictures after all... It had to do some upgrading since i went from LR5 to LR6, but everything seems ok.
So where do I control exactly where LR6 saves it ".lrcat" file?
I don't know what XMP sidecar files does, where should I read up on what that option offers? Something i should consider?
Lightroom saves all your work and developments in the catalog. Presets and Templates are saved to special folders.
What goes where: Preference file and other file locations | Lightroom CC and 6
Read about XMP here: Metadata basics and actions in Lightroom