The SqlParameterCollection only accepts non-null SqlParameter type objects, not DBNull objects

Why don't you start over again and do some proper validation before getting to this point? You should never ever start creating objects and stuff if there is no need to do so. So, make yourself a favor and add a validation method like in

private bool IsValid()
{
    return !Controls.OfType<TextBox>().Any(c=> String.IsNullOrEmpty(c.Text));
}

and then add a call just before the code to construct the sqlcommand and parameter collection

if(IsValid())
{
    // do you stuff here
}
else
{
   MessageBox.Show("Please complete the fields", "Information...", 
                   MessageBoxButtons.OK, MessageBoxIcon.Warning, 
                   MessageBoxDefaultButton.Button1);
}

Keep in mind this is not tested, I don't have VS right now and all is written manually, so maybe Control collection is not accessed that way.

First of all, you need to look for whether the value property of any of the parameters is DBNull. You're trying check whether parameter object itself is DBNull, but you should be looking at the Value property. You can do that like this:

if ( cmd.Parameters.Any(p => DBNull.Value.Equals(p.Value)) )

Secondly, the .Text property of your textbox controls will never be null. At worst, it will be the empty string. So what you really want is code like this:

if ( cmd.Parameters.Any(p => string.IsNullOrWhiteSpace((string)p.Value)) )

Finally, as an aside, even if the .Text property could be null, this is not the same as DBNull. They are two different things.

Clean and effective approach. Will help you in later developments. Change your code something like this:

1. Create a class called student and inside that class create properties for FirstName, LastName and others as required. Something like this:

   public class Student
   {
       public int StudentId {get;set;}
       public string FirstName {get;set;}
       public string FirstName {get;set;}
       public string MiddleInitial{get;set;} // upto ContactNumber or as required.
    }
   

2. Create a separate method for assigning parameters to SqlCommand. Here in these methods you can also put validations if you required using ternary operations i.e ?,:

   private void CreateParameterList(ref Student s, ref SqlCommand cmd)
          {
             var parameters = new []
                                  {
                                    new SqlParameter("@FirstName",s.FirstName),
                                    new SqlParameter("@LastName",s.LastName),
                                    :
                                    :
                                     new SqlParameter("@ContactNumber",s.ContactNumber)
                                   }
             cmd.Parameters.AddRange(parameters);
          }
   

3. Create a Method for Save and pass the above class as parameter. You can also create a separate partial class in name of Student so as to access the members using same instance. Call the method in step 2, so as to use the parameters.

   protected void MySaveFunction(Student s)
   {
       using(SqlConnection con= new SqlConnection(your_Connection_String))
       {
           using(SqlCommmand cmd = new SqlCommand())
           {
               cmd.CommandType = CommandType.Text/StoredProcedure;
               // it depends on what you are using
               cmd.Connection = con;
               cmd.CommandText=Your Query or Name of SP;
               con.Open();
               CreateParameterList(ref s, ref cmd);
               try
               {
                   int i = cmd.ExecuteNonQuery();
                   if(i>0)
                   {
                       //Show Success or return Success
                   }        
               }
               catch(SqlException sqlex)
               {
                   //catch and log exception
               }
               finally
               {  con.Close(); con.Dispose() }
           }
       }
   }