Has West Virginia University ever won a Football National Championship?

No, and they've only played for one once (1989 Fiesta Bowl, a 34-21 loss to Notre Dame.)

source: cfbdatawarehouse.com

Actually Croswenthy is technically wrong. WVU has played for the National Championship twice. Once in 1989 (the Fiesta Bowl) and again in the 1994 Sugar Bowl. The luck of the 1993 squad was just like the 1988 squad in their national title game. The Mountaineers would play the Florida Gators for a share of the national title but lost to Florida 41-7.