Hoping to help a few others get past MS' solipsist thought, here is an update:
1) Disabled ESET - Big Help
2) Disabled/Enabled Win Firewall - No difference
3) LAN Configuration - Took Out ESET;
Added IPv6Result:
1) Now 6-Core can see Quad-Core
2) Successfully transferred important files (so I can work at least) from "Documents" after copying them from the H directory of the Quad-Core to "Documents" on Quad-Core (real damned progress, going via one's kneecap to get from the shoulder to the hand!) - THIS TIME, THOUGH, FILE TRANSFER DID NOT STALL.
Existing Problems:
1) Quad-Core cannot see 6-core via Explorer but is on the Network Map (go figure)
2) I still cannot transfer files from viewed partitions on Quad-Core to 6-Core without moving them first to Documents on the Quad; I am told I "Do Not Have Permission From My Adminstrator (I am the damned Administrator!) - "Permissions" granted to ALL w/out restriction.
Movement From 6-core to Quad not possible at all - of course.
A small victory but still not there yet - even to circa 1995 modernism.

Quick Question: Why do the Smily's on out site really, really suck so bad? Just a question, OK.