You may be looking for the "David Cook" that served in Company I, 36th Virginia Infantry. He was captured at Cloyd's Mountain on 5/9/1864 and imprisoned at Camp Chase, where he died on February 6, 1865 from smallpox. Buried at Camp Chase Confederate Cemetery in Grave #1071.

I can't find a "David Cook" on the 1850 or 1860 Census of Tazewell County, but see men by that name in Giles, Wyoming and Montgomery Counties....same neck-of-the-woods.