Here's a little more while I was on hold.
Don't be disappointed if he wasn't at Gettysburg, family history when passed down is usually crap. I have disproved all mine.
I would check the Vermont regiment history, as they had great losses and were in some serious battles. I believe they had the greatest losses in the war. Bottom line is he answered the call, and saved the republic.
N.H. 14th Regiment
Organized at Concord and mustered in September 24, 1862. Ordered to Washington, D.C. Attached to Grover's Brigade, Military District of Washington, to February, 1863. Jewett's Brigade, 22nd Corps, Defenses of Washington, to June, 1863. Garrison of Washington, D.C., 22nd Corps, to March, 1864. Unattached, Defenses of New Orleans, La., Dept. of the Gulf, to June, 1864. 1st Brigade, 2nd Division, 19th Army Corps, Dept. of the Gulf, to July, 1864, and Army of the Shenandoah, Middle Military Division, to January, 1865. 1st Brigade, Grover's Division, District of Savannah, Ga., Dept. of the South, to March, 1865. 1st Brigade, 1st Division, 10th Army Corps, Dept. of North Carolina, to May, 1865. Dept. of the South to July, 1865.
SERVICE.--Picket and patrol duty along Upper Potomac, Defenses of Washington, November, 1862, to April, 1863. Provost duty at Washington, D.C., until February, 1864. Ordered to Harper's Ferry, W. Va., February 3, thence moved to Cumberland, Md., and return to Washington February 25. Ordered to New Orleans, La., and sailed from New York March 20. Duty at Camp Parapet, Carrollton, Jefferson City and along Lake Pontchatrain until June. Ordered to Morganza, La., June 7. Movement to Fortress Monroe, Va., thence to Washington, D. C., and to Berryville, Va., July 13-August 19. Sheridan's Shenandoah Valley Campaign August to December. Battle of Winchester September 19. Fisher's Hill September 22. Battle of Cedar Creek October 19. Duty at Kernstown and other points in the Shenandoah Valley until January, 1865. Moved to Washington, D.C., thence to Savannah, Ga., January 8-20, and Provost duty there until May 6. March to Augusta, Ga., May 6-14. Return to Savannah June and mustered out July 8, 1865.