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.
It seems the specs are fine but you didn't mention other specs like CPU and if you are using 32bit or 64bit I have experienced before when using Bitcoin core with 32bit which is too buggy and can't able to use it.
Anyway, have you recently force to shut down your PC without closing Bitcoin core while syncing? It will always end up with data corruption if you didn't properly shut down your core.
The logs are suggesting to use -reindex it must be work but since you already tried it how did you perform -reindex?
Did you edit the bitcoin core shortcut under target add -reindex? Or you run bitcoin core through command prompt with -reindex?
Adding this if you are using 32bit read this
https://bitcointalk.org/index.php?topic=5139689.msg50915664#msg50915664 posted by Achow101 you might need to build a 32bit one to make your core work properly.
BitMaxz -- CPU is AMD Phenom II X4 960T 3.4 GigaHz, 64 bit W7. Sometimes I have shut it down by accident before closing bitcoin core.
I performed -reindex by adding it as a flag to the Windows shortcut that opens bitcoin core. So, I use the flags: -datadir=F:\Bitcoin -reindex tacked onto the bitcoin-qt.exe call in the shortcut. My W7 box connects to the NAS this way -- F is a samba share.