SF_10.1, SF_10.2, SF_11.0, SF_11.1, SF_11.2, SF_12.0, SF_12.1, SF_12.2, SF_13.0, SF_13.1, SF_13.2, SF_13.3, SF_14.0, SF_14.1, SF_14.2, SF_14.3 - https://docs.sitefinity.com/application-status-page-in-continuous-integration-scenarios

EnsureSitefinityIsRunning.ps1

param([String]$url="http://localhost", [String]$successOuput="SUCCESS", [Int32]$totalWaitMinutes=10)

$elapsed = [System.Diagnostics.Stopwatch]::StartNew()

$statusUrl = ($url + "/appstatus")
Write-Warning ("Attempt to start Sitefinity up: " + $statusUrl)
$retryCount = 0;

try 
{ 
  Write-Warning ("Retry: " + $retryCount)
  $retryCount++;
  $response = Invoke-WebRequest $statusUrl -TimeoutSec 1800 -UseBasicParsing

  if($response.StatusCode -eq 200)
  {
    Write-Warning ("Sitefinity is starting ..." + $statusUrl)
  }  

  while($response.StatusCode -eq 200)
  {    
    Write-Warning ("Checking Sitefinity status: " + $statusUrl)
	Write-Warning ("Retry: " + $retryCount)
	$retryCount++;
    $response = Invoke-WebRequest $statusUrl -TimeoutSec 1800 -UseBasicParsing

    if($elapsed.Elapsed.TotalMinutes > $totalWaitMinutes)
    {
	  Write-Warning ("Sitefinity did NOT start in the specified maximum time")
      break
    }

	Start-Sleep -s 1
  }
} 
catch 
{
  if($_.Exception.Response.StatusCode.Value__ -eq 404)
  {
    $response = Invoke-WebRequest $url -TimeoutSec 120 -UseBasicParsing

    if($response.StatusCode -eq 200)
    {
      Write-Warning ("Sitefinity has started after " + $elapsed.Elapsed.TotalSeconds + " second(s) - " + $successOuput)
    }
    else
    {
      Write-Warning "Sitefinity failed to start"
    }
  }
  else
  {
    Write-Warning ("Sitefinity failed to start - StatusCode: " + $_.Exception.Response.StatusCode.Value__)
	
    Write-Warning $_|format-list -force
	  Write-Warning $_.Exception|format-list -force
  }
}

On line 27, should it read:

$elapsed.Elapsed.TotalMinutes > $totalWaitMinutes

instead of the current:

$elapsed.Elapsed.Minites > $totalWaitMinutes

"Minites" isn't a property on the StopWatch object, so it is always represented as $null, so the comparison to $totalWaitMinutes (10) is always false.