That directory is usually created in the installation process. Was the database created properly? You could manually copy the webassist directory from the install/webassist/ directory if your database was created properly... however I think it must have created the webassist directory if you are able to get to that point before having problems.
Most likely this is a permissions problem with the /webassist/ directory that was created on the server. Try changing the permissions on that directory from '777' to '755'... that has helped others that have reported the same issue.