Did you try loading an existing save? If you don't have any previous saves, you can
download one and extract it into your '..\Documents\Larian Studios\Divinity Original Sin\PlayerProfiles\<ProfileName>\Savegames' folder.
You could try playing the game from a new OS user account.
Did you try a clean re-install of the game? With Steam you can backup the game, delete local files, make sure everything is removed from the install folder, and then restore the backup. That may help without having to redownload the game again.
Check the Event Viewer; the error code or faulting module listed for the crashes may help narrow down what the problem is, or (with a web search) give additional suggestions.
- click Start (or WinKey-W in Win 8), then type "event viewer" (or just "ev") into the search box
- after starting the Event Viewer, expand 'Windows Logs' in the left column and select 'Application'
- in the center column, look for a recent error (maybe sort by Date and Time) for the game
- look at the information under the 'General' tab below the list of events, starting with "Faulting application name..."
