He served throughout the entire Revolutionary War, as a lieutenant in Captain Hopkins' company, 2nd Connecticut Regiment. He is mentioned in Records of the Revolutionary War as a lieutenant from Connecticut who "served to the end of the war and acquired the right to half-pay, commutation, and bounty land under the preceding Acts of Congress."
According to Revolutionary Soldiers, "Eliakim Barnum | an officer of | the Revolution | died Sept'r 18, 1835 | Ae. 86 Y'rs. | Sarah | his Wife died Nov. 20th, 1825; | Ae. 73 Y'rs. | Jamesville cemetery. The name is in the 3d Dutchess Co. regiment, but he was not a N. Y. officer. In Col. Zebulon Butler's 2d Conn. regiment, Ensign Eli Barnum ranked as 2d lieutenant. As names were often shortened in common use, this was probably his rank. In 1790 he was in Ballston, N. Y." This passage appears to refer to two separate persons, since some of the data applies here but some does not. The 2d Dutchess Co. regiment is confirmed by other sources; the 3d is not. This Eli married Eunice, and was still married to her after the marriage date to Sarah given above. Eli was certainly present at Ballston, where his two children were born in 1780 and 1782.