Well, you should use the method "ReadLine()" from the StreamReader in a loop. When you receive an empty line, simply check if the string obtained from ReadLine() is empty. If it is, ignore the line.
Try something like:
StreamReader input = new StreamReader("...");
String line = null;
do
{
line = input.ReadLine();
if (line == null)
{
return;
}
if (line == String.Empty)
{
continue;
}
// Here you process the non-empty line
} while (true);