Hi,
Mary initially noted: My Grand Father William T. Bennett fought in the Civil War.... I think he was in the 4th Infantry..
Richard noted: Bennett, William F. T., 1st Lt., Capt. Co. F. 9th La. Infty. (NOTE - this Bennett is in the 9th La)
Alan noted: William T. Bennett enrolled in Capt. John Bunyan Taylor's Co. "F", 4th Louisiana Regiment (later Co. "I"). (This matches up with Mary's initial comment, and her recollection.

Looking at Booth's for Bennett the following is noted:
Bennett, William T., Pvt. Co. I. 4th La. Infty. En. May 25th, 1861, Camp Moore, La. Present on All Rolls to Aug., 1861. Roll for March and April, 1862, "Wounded at Shiloh, April __, 1862." Roll for Nov. and Dec., 1862. "Absent. Was Wounded at Battle of Baton Rouge. Not Reported for Duty Since." Rolls from May, 1863, to Aug. 31st, 1864, "Present." Roll for Aug. 31st. 1864, to Feb. 28th, 1865, "Killed on Aug. 31st, 1864, at Jonesboro." Federal Rolls of Prisoners of War Captured Jonesboro, Ga., Aug. 31st, 1864. On Hospl. Register, "Admitted Sept. 10th, 1864, to G. F. Hospl., Dept. of the Cumberland. Atlanta, Ga." Sent to Barracks Oct. 23rd, 1864. Forwd, to Military Prison, Louisville, Ky., from Nashville, Tenn., Nov. 25th, 1864. Recd. at Camp Douglas, Ill., Nov. 26th, 1864. Paroled at Camp Douglas, Ill. Forwd. to City Pt., Va., for Exchange March 14th, 1866. Recd. at Boulware's and Cox's Wharf, James River, Va., March 18th to 21st, 1865, and Exchanged.

Which is very similar to what Alan wrote.

JIM T