Well one option is the free
CCleaner. It has an "Issues" button on its left side, and a checkbox in Issues is to detect "Obsolete Software."
A second option is the Disk CLeanup utility in Windows System Tools. Click its "More Options" tab, then its "Installed Programs Cleanup" button. You said a lot of old junk isn't registered in the new installation, but you still could run this just to see if it detects any of the junk. Wouldn't hurt.
A third option is to use Windows Explorer to simply visually inspect the C:\Program Files\)list of programs) and compare that to what you see displayed in Windows Control Panel \ Add or Remove Programs. It'd be pretty easy to just look at thiose two lists. You'd delete from the Program FIles tree any folders for programs not appearing in the Windows Control Panel \ Add or Remove Programs.
Alternatively, instead of using Windows Control Panel \Add or Remove Programs, you could also use CCleaner/Tools/Uninstall to display the properly installed programs. Then in just delete the folders for any other programs that do not appear on that list, but that do appear in C:\Program Files\.
So there are some free ways to help you.
Others on this board insist I'm wrong, but nevertheless if it were me, after deleeting the old programs I'd run a registry cleaner & defrag.
It's good of you to give tech support to your dad. I'm sure he appreciates it.