Get-Content grabs data and dumps it into an array, line by line. Assuming there aren't other special requirements than you listed, you could just save your content into a variable?
$file = Get-Content c:\file\whatever.txt
Running just $file
will return the full contents. Then you can just do $file.Count
(because arrays already have a count method built in) to get the total # of lines.
Hope this helps! I'm not a scripting wiz, but this seemed easier to me than a lot of the stuff above.