Why would the sharing button on my dashboard be "gray" and inaccessible to me?  This is preventing me from sharing my dashboard with others at my agency.

It sounds like your security settings have been restricted from sharing dashboards.  If you need to be able to do this, ask the supervisor to amend your security which is loacted under configuration.  Open up the group that you are a member of and there is a check box for dashboard access.  When this is highlighted, there is an options box available which contains a checkbox for sharing dashboards.  Check this and log off and on and it should work fine.