Thank you for the numerous list of suggestions of other things for me to investigate (rather than asking for assistance with the bitcoin core client here.)
My PC has 6 Gb of RAM, it does have a SSD (which all programs, including the Bitcoin Core, run from), the OS is Windows 7. The NAS works fine with all the other devices connected to it. Someday I guess I will benchmark it in my spare time.
There surely must be some other detail(s) some of you could find for me to not expect the bitcoin core software to work and give up on the question I asked?