Hi Grobe,
So you're saying you did not upgrade Inkscape at all. You got a brand new Windows 10 computer. So that means you would have either used some kind of transfer program, to transfer files like images (as windows calls them "Pictures" and "Documents"). Or you would have manually copied them onto a cd or usb drive, and moved them into the new computer.
That's where I would look first -- how did you take the files from the old computer and put them on the new one? If something has happened to the images, that's likely when/where it happened.
But hopefully you still have either the old computer with the intact images/files, or backups somewhere?
Or do you mean you made some new drawings in Inkscape, after you installed inkscape on the new computer?
When you said you got to keep the old hard drive, how does that work? Was it an external hard drive? Or else, how do you access it?
Do you mean that you accessed the old hard drive on the new computer, and you used Inkscape while it was installed on the old hard drive, but you're logged on to the new computer? I guess I wouldn't be really surprised if that kind of arrangement is problematic!
I don't think it would help to install the 64-bit Inkscape, because as you probably know, the 32 bit programs will run on a 64-bit system. So there's no reason to think that should help.
However, I do think it would help to install Inkscape on the new computer, and not use it from the old hard drive. Or maybe the portable version of Inkscape would work better for that kind of arrangement. I'm not sure, I'm not very familiar with the portable version.