Workers are concentrating their efforts on broken and downed lines and poles scattered throughout remote mountains far from even dirt roads.
The Dec. 19 weekend storm dumped more than a foot of snow across the two states, with some areas seeing around 2 feet.
Utility crews in Virginia suffered a setback in restoring power to all customers when an ice storm moved through on Christmas Eve.
In Virginia, Dickenson County has the most customers without power at 3,000.
In West Virginia, McDowell County had the most at 560.