Use Get-Content -Read $nLinesAtTime
to read your file part by part:
$nlines = 0;
# Read file by 1000 lines at a time
gc $YOURFILE -read 1000 | % { $nlines += $_.Length };
[string]::Format("{0} has {1} lines", $YOURFILE, $nlines)
And here is simple, but slow script to validate work on a small file:
gc $YOURFILE | Measure-Object -Line