I actually got this to work last night in XP. Download the patch before you start. Run the DOS version of the install; navigate via explorer on the CD until you see an MS-DOS icon and click on that. On my machine, it ran in a window but was fine.
Now, after you install, unzip the patch onto the hard drive where the game was installed (probably c: ; I used a different letter drive and it seemed fine).
Then, when you want to run the game, navigate into where you installed the game and look for the birthright win .exe file; I think its winbr.exe. Click on that and away you go.
If you press F2 while playing it seems to run fine in full-screen.
BB