What is the value of a gold 1776-1976 quarter?

Gold-plated but not gold. A lot of private companies took standard copper-nickel Bicentennial coins, plated them, and sold them as "collectibles" during the celebrations in 1975 and 1976. But once the party was over, the bottom dropped out of the market for them, plus they're considered altered coins, so they have very little value to coin collectors.