Conn was born on November 13, 1805, in Jefferson County and was the son of Richard Isaacs Wilkes Conn and Priscilla Morgan Conn. Little is known of his early life and education, except that his father died when he was six years old. Conn executed a marriage bond in Page County on February 23, 1835, and on that date or soon thereafter married Ann Eliza Almond, who died on October 30, 1836. They had one daughter. On June 24, 1841, Conn married Sibelia A. J. Ladd, of Henrico County. Of their four sons and two daughters, only two sons and one daughter survived childhood. Sibelia Conn died of bronchial consumption, probably tuberculosis, on December 31, 1853, and on December 8, 1859, Conn married Mary E. Russell, of Frederick County. They had one son before she died on July 6, 1871.
Conn lived near Mount Jackson, in Shenandoah County, and in 1831 inherited two tracts of land in Page County from the paternal uncle for whom he had been named. Conn’s long public career began with an appointment as deputy sheriff of Shenandoah County on March 12, 1832. The following year he was both deputy sheriff and deputy coroner. Conn served as an officer in the 13th Regiment of the Virginia militia, by September 1832 until August 1833 as major, from August 12, 1833, to April 11, 1835, as lieutenant colonel, and after that date as colonel. Offended by the General Assembly’s promotion of the regiment’s much-younger and less-experienced lieutenant colonel to command of the brigade, Conn resigned his commission on January 21, 1854.
Between 1838 and 1841 Conn represented Shenandoah County for four consecutive one-year terms in the House of Delegates, where he sat at various times on the committees on Agriculture and Manufactures, on Militia Laws, on Trade and Mechanic Arts, to Examine the Enrolled Bills, and to Examine the Public Armory. He became a Shenandoah County justice of the peace on January 13, 1842, and served consecutive two-year terms as sheriff beginning in June 1852. Conn was a founding director and superintendent of the Mount Jackson Manufacturing Company, a woolen manufactory incorporated in 1848 and also authorized to cast farming tools, ironware, machinery, and stoves. He paid taxes on four slaves in 1850 and a decade later owned one, a sixteen-year-old male slave whom he probably hired out.
Campaigning as a secessionist who believed prompt action was required to protect, Conn won election by a large majority on February 4, 1861, as one of two delegates representing Shenandoah County in the state convention called to debate the issue of secession. He spoke only once on the convention floor, to seek clarification of a procedural question. Conn voted for secession on April 4, and again on April 17, signed the , and returned to for the second and third sessions in June and November 1861. He delivered a compelling speech at Columbia Furnace, near Woodstock, in May 1861 while trying to raise a volunteer company for . On June 11 he received a gubernatorial appointment as colonel in the Provisional Army of Virginia. Conn’s command, the 43rd Virginia Volunteers, was stationed at on September 30 of that year, but none of its muster rolls or other records survive. He had begun serving as Shenandoah County clerk by October 1863 and the following year was elected to fill the post for a term ending on July 1, 1870, but he stepped down in 1865.
After the Civil War, Conn farmed approximately 310 acres in Shenandoah County and served as trustee of the Green Hill Academy. The absence of his name from local records after 1880 suggests he may have left the county to live with one or more of his children. Conn died at the Warren County residence of his daughter on March 31, 1887. He was buried in Green Hill Cemetery, in Luray, Page County.