This was fixed after a post in the Steam forums (presumably mod related). Normally I check here first, but that day I missed doing so until later.

Anyway, in case anyone else runs into this problem, I'll copy most of my Steam reply here:

With a shovel in a character's inventory, you should just have to left click on a mound / grave to dig (mouse cursor changes to a gears version, the same as interacting with a well or sign post, etc).
Double clicking on the shovel in the inventory, or right clicking and selecting Use, will have the character dig at the current location, regardless of whether there is a mound or not (useful to look for something even if a character doesn't have the perception to 'spot' it).

Try verifying local files, though reinstalling should have fixed any issues with missing or corrupt files, especially if you made sure the install folder was removed (or empty) after uninstalling, or installed to a different location.
In the (optional) Galaxy client, select the game in the left column, then click on the More button, and in the Manage menu select 'Verify / Repair'.

If you create a new profile, start a new game on the lowest difficulty, get through the first fight on the beach and grab the shovel from the waypoint, can you use it from the inventory, or digging the mound towards the 2 drunk soldiers guarding the bridge?