So start with the debugger and look at exactly what is going on.
Initially, change that line to just the declaration:
public string _connectionString = null;
and in your Seller class constructor add this:
var o1 = ConfigurationManager.ConnectionStrings["seller"];
var o2 = o1.ConnectionString;
_connectionString = o2.ToString();
Then put a breakpoint on the first line and step through, using the debugger to look at the values - when you know which one is null, you can start looking at why - but until you know that, you are just guessing.
We can't do this for you - we don't have access to your machine or the web.config file.