How can I connect to an Oracle database as SYS using an ADO connection string?
You can't connect as SYSDBA using standard System.Data.OracleClient, as stated by this post : http://forums.microsoft.com/MSDN/ShowPost.aspx?PostID=2245591&SiteID=1.
You can do that using ODP .NET (Oracle Data Provider for .NET), or other third parties library. If you're planning to build serious Oracle Application on .NET, I suggest you at least look at ODP.NET
I'm not sure what you mean by connecting as a SYS, but there here is a link to sweet repository of connection strings. I hope you can find your answer there.
Oracle Connection string sample
You must have your Oracle SID defined in your TNSNames file. Which is the data source.
Data Source=oracl;User Id=userID;Password=password;Integrated Security=no
If you are using Visual Studios you can add a data source in the Sever Explore and it will give you the connection string.