Assuming your start/end "points" are actually lines, you basically need to read from the start and skip the lines until you reach the right one. Here's an easy way of doing it using File.ReadLines
:
var lines = File.ReadLines(inputFileName)
.SkipWhile(line => line != "[[START SourceSystemHost]]")
.Skip(1) // Skip the intro line
.TakeWhile(line => line != "[[END SourceSystemHost]]");