Your first job would be to launch Fiddler and see if the values are actually sent to the server. This is a generic advice that should be used every time any similar problem arises.
In your case the problem might be that your <checkbox>
tags do not include value
attribute so they will just send an empty value to the server.
Also you should provide the arguments to Html.BeginForm
so that the form generates the correct target action.
Also remember that checkbox-es that are not checked, are never sent to the server in POST data.