Parunak was born in Freehold, New Jersey, July 10, 1910. He attended Ursinus College in Collegeville, Pennsylvania, graduating in 1933 with a B.S. degree in math and physics.

Parunak joined the US Navy Aviation Cadet program in 1935 and received his wings in December 1936. He was assigned to the fleet in Coco Solo, Canal Zone, Panama as a P2Y-2 pilot.

From 1939 until June 1941, Parunak was a pilot/instructor at Naval Air Station Pensacola, Florida. Next, he was reassigned to VP-93 at Naval Air Station Norfolk, Virginia. After Pearl Harbor he was assigned to PBY-5s and moved to Naval Air Station Argentia, Newfoundland for convoy escort and anti-submarine warfare.

In 1942 Parunak, then a lieutenant was named head of a three-plane unit of PBY-5As at Bluie West 8, a base in northwestern Greenland above the Arctic Circle. He was under the command of U.S. Army Air Corps Lt.Col. Bernt Balchen, the noted polar aviator and explorer. These bases were established to allow the U.S. Army to route supplies to England over Greenland to reduce contact with German U-Boats. The area made for difficult flying conditions. Parunak frequently flew Balchen and his rescue team to crash sites. Between June 10 and July 18, 1942 they rescued the crews of three B-17s and one AT-6.

Parunak earned recognition as the first pilot to land and take off from the Greenland ice cap, during the rescue of the crew of the US Army Air Corps. B-17-E 9032 My Gal Sal, which crashed June 27, 1942. His efforts in this rescue earned Parunak the Distinguished Flying Cross. The B-17, recovered and restored, is now on display in the National World War II Museum in New Orleans.

From 1942–45 Parunak was assigned to various squadrons including commands of anti-submarine patrols in the North Atlantic and Mediterranean. Near the end of the war, Parunak married Orianna Van Dyke. After the war, he stayed in the navy and in 1955 was promoted to the rank of captain. Parunak took command of the U.S. Naval Air Station at Atsugi, Japan in 1958. For his contributions in re-building American-Japanese relations, Emperor Hirohito ordered Captain Parunak decorated with the Third Order of the Sacred Treasure. Parunak retired from the Navy in 1961 then worked for General Electric Space Research in Valley Forge, Pennsylvania for ten years as manager of facilities and maintenance.