I would try giving it 777 permissions then running through the install. After that, you can revert the permissions back to be more restrictive. Then make sure the imagesupload folder at least has write permissions.
Basically, the installer writes the connections file dynamically and also creates the imagesupload folder. After installing, the imagesupload needs write permissions so that new images can be added to the content areas.
It also depends on the web server for how these permissions work out, some shared servers run all users as the same user, which is not quite ideal. This sounds like the case you are in. Ideally, the web server will have separate instance running for each user to keep everyone better separated.