GOG's version of Divine Divinity does not use DosBox so that would not be the problem. (No version does IIRC)
Not knowing what your OS is makes it difficult to diagnose but I will assume it is Vista or Win 7. If you turned off UAC before installing the game, installed as an admin (right clicked the setup.exe and clicked "Run as an administrator") and installed in a directory outside of Program files then my first suggestion is to right click the game shortcut, click Properties, click the Compatibility tab and check mark "Run this program as an administrator".
Not running the game as an admin can cause problems since some disk read / writes can be blocked. I also suggest checking the "Disable visual themes" and "Disable destop composition" which is also located on the Compatibility tab.
Not having the latest video drivers caused some odd behavior on my first DD install. Updating to the newest fixed some graphics problems.
Click here for ATI Click here for Nvidia Click here for Intel Here is a link for my basic suggestions for installing DD. Note the info about firewalls at the bottom. If the above does not give joy then try playing with the firewall off. If that fixes the problem make the div.exe a trusted program in your firewall. Make sure you enable your firewall after this test.
I got some corrupted saves using the "quick" save method (CTRL-S) but have not had any further save corruptions since I started using just the S key to save. Hope this helps . . . =)