James,

I can't speak for how "absolutely" complete this roster is, but here is a roster of Company B or the 4th Minnesota incl their enlistment date.

Jim Martin

George Abbott 2 Oct 1861
Francis J Allgauer 2 Oct 1861
Knud Anderson 31 May 1864
Theodore Anderson 31 May 1864
Michael Anderson 31 May 1864
Rufus L Applin 26 Sep 1861
Andrus B Applin 26 Sep 1861
William Armes 26 Sep 1861
Josiah Armes 26 Sep 1861
Shobal D. L. Baldwin 26 Sep 1861
Francis M Beedle 30 Sep 1861
Orpheus G Belden 15 Aug 1864
John M Bellsfield 30 May 1864
Christian Bender 8 Mar 1865
Andrew Beck 30 May 1864
Marion Blacker 16 Oct 1864
Louis Jackson 18 Mar 1865
Charles P Booth 26 Sep 1861
Truman Booth 22 Mar 1862
Alonzo L Brown 26 Sep 1861
Charles H Brown 26 Sep 1861
John N Bradford 26 Sep 1861
Arthur Bradley 16 Aug 1864
Samuel B Brown 28 Feb 1864
James Braley 16 Aug 1864
Joseph Brebic 30 Mar 1864
Judson Burrows 26 Sep 1861
Joshua Burton 16 Aug 1864
Leonard A Caldwell 26 Sep 1861
John Chimblom 12 Dec 1861
William T Churchill 26 Sep 1861
Edmund P Churchill 26 Sep 1861
John K Cochrane 24 Sep 1861
Leo Cook 30 Sep 1861
Charley Crane 15 Aug 1864
Stephen D Dammon 26 Sep 1861
John Dercks 3 Mar 1864
Henry Doane 16 Aug 1864
James W Dunn 26 Sep 1861
Thomas Ellsworth 26 Sep 1861
Michael Engel 30 May 1865
Holver Evanson 6 Jun 1864
Patrick Fallon 26 Sep 1861
Thomas Fallon 26 Sep 1861
Richmond Fadden 20 Mar 1865
Charles B Fenn 26 Sep 1861
Fayette E Ford 26 Sep 1861
John R French 26 Sep 1861
John Frank 18 Oct 1861
Samuel I Fuller 28 Feb 1864
William W Getchell 26 Sep 1861
Peter Geoghegan 26 Sep 1861
John Goetz 30 May 1865
Charles H Goodrich 28 Feb 1864
George W Gilson 26 Sep 1861
Joseph A Goding 26 Sep 1861
John B Grover 26 Sep 1861
View Record Knudt Gunderson 26 Sep 1861 Minnesota Union
Francis W Hanscom 30 Sep 1861
Willard L Harris 30 Sep 1861
Henry P Hatch 22 Nov 1861
Asberry Hartshorn 16 Aug 1864
Hiram Hazleton 20 Mar 1865
David W Hern 26 Sep 1861
Michael Hemerich 2 Oct 1861
Joseph Heck 2 Apr 1862
William Hillburg 2 Oct 1861
Charles Hopkins 26 Sep 1861
Anson Hopkins 26 Sep 1861
John P Hunter 26 Sep 1861
Morris Hunter 16 Aug 1864
Edwin Jewett 26 Sep 1861
Ole Johnson 26 Sep 1861
Jonas Johnson 30 Sep 1861
John Johnson 26 Sep 1861
William H Jones 16 Aug 1864
Albert Johnson 13 Apr 1862
William Knable 30 Sep 1861
Gustave Kohler 18 Mar 1865
Jacob Koons 30 Sep 1861
Herman Koofman 12 Dec 1861
Reuben Lamphear 26 Sep 1861
Thompson Laraway 26 Sep 1861
James Loughnane 26 Sep 1861
Joseph Lamb 15 Aug 1864
David Lapier 20 Aug 1864
Henry Lanners 17 Mar 1865
Joseph Lappo 20 Mar 1865
Martin Luther 30 Sep 1861
Luke Marcile 27 Sep 1861
Frank Meyer 30 Sep 1861
James McCartney 26 Sep 1861
Michael McCann 26 Sep 1861
James A McLeary 2 Oct 1861
Dougal A McDougald 26 Sep 1861
Harvey McQuillan 15 Aug 1864
Chester G Mickel 26 Sep 1861
Bernhard Moormann 12 Dec 1861
James Neil 26 Sep 1861
Ole Nelson 26 Sep 1861
Townsend G Nichols 26 Sep 1861
Edgar Nichols 26 Sep 1861
Peter Oleson 3 Mar 1864
Frank Oleson 22 Dec 1864
Alf Oleson 6 Jun 1864
Nels Oleson 20 Jun 1864
John P Parson 2 Oct 1861
View Record Henry Peters 20 Feb 1862 Minnesota Union
Adam Pfeffer 17 Mar 1865
William B Phelps 15 Aug 1864
Andrew I Phillips 20 May 1864
Marvin Pond 2 Oct 1861
Edwin Potts 26 Sep 1861
Francis M Reynolds 30 Sep 1861
Charles Reich 9 Mar 1865
Daniel Rhodes 26 Sep 1861
Frank Rushmire 26 Sep 1861
Christopher Sanken
Martin V. B. Scribner 15 Aug 1864
Ole Severson 13 Jun 1864
Andrew Sorrenson 6 Jun 1864
Irvin Shaw 15 Aug 1864
William H Shadwell 15 Aug 1864
Champion Shilling 20 Feb 1864
Charles H Stinchfield 26 Sep 1861
Joel Stevens 16 Aug 1864
Ezra M Stacy 30 May 1864
Charles W Sutton 15 Aug 1864
Swan Swanburg 30 Sep 1861
John Thompson 26 Sep 1861
Thomas Thompson 11 Mar 1865
Charles G Topping 26 Sep 1861
Luther W Turner 16 Aug 1864
Turban Trinson 31 May 1864
Horatio Vaughan 3 Sep 1864
Anthony Vogel 8 Mar 1865
Sylvanus Wakefield 26 Sep 1861
Daniel E Way 18 Aug 1864
James F Withee 26 Sep 1861
Abraham P Williams 30 Sep 1861
James A Williams 2 Dec 1861
John Yager 25 Jul 1864
Edward A Zeibarth 30 Sep 1861
Charles Zeibarth 30 Sep 1861
James C Edson 2 Oct 1861
Dennison M. G. Murphy 22 Nov 1861
Ransom A Judd 2 Oct 1861
Cyrus L Snyder 9 Jul 1862
Rudolph Borgersrode 2 Oct 1861
William K Vickroy 2 Oct 1861
Orlando Graham 26 Sep 1861
Ahimaaz E Wood 20 Sep 1864