Check multiple conditions, then if all are false do something - powershell

Question

Bit of background...
I'm trying to write a script which will run constantly. I need to it check to see if the Queue directory has an XML file in it, if it does, then send an API call to start some servers.
I've got this part sorted and it works.
I'm having issues with the second part where I need it to send another API Call to shutdown the servers if the following conditions are met;
Queue Directory must be empty
Running Directory must be empty
The time between the servers starting and stopping must be to the nearest hour (its AWS so they charge by the hour, there's no point in stopping a server if its only been running for a few mins as we'll still be charged for the full hour. Then if we need to start again, we'll be charged another hour.)
Here is what I have so far:
$QueueDir = "D:\Test"
$RunningDir = "D:\Test\copydir"
while (!(Test-path $QueueDir\*.xml)) {Start-Sleep 10}
Write-Host "Starting Servers, API NORMALLY GOES HERE"
$Starttime = (Get-Date)
Write-Host "Started Servers # $Starttime"
Start-Sleep -Seconds 30
while (!(Test-Path $rundir\*.xml)) {Start-Sleep 10}
$now = (Get-Date)
$timespan = (New-TimeSpan -Start $Starttime -End $now)
if ( (Test-Path $QueueDir\*.xml) -or (Test-Path $RunningDir\*.xml) -or ($timespan.Minutes -gt 50 -and -lt 55) ) {
Write-Host "Stopping Servers, API NORMALLY GOES HERE"
$StopTime = (Get-Date)
Write-Host "Stopped Servers # $Stoptime"
}

Answer 1

This $timespan.Minutes -gt 50 -and -lt 55 is not valid PowerShell logic. You have to provide a value expression after -and. You would receive an error like this:
You must provide a value expression following the '-and' operator.
+ CategoryInfo : ParserError: (:) [], ParentContainsErrorRecordException
+ FullyQualifiedErrorId : ExpectedValueExpression
So you would need to use it like:
$timespan.Minutes -gt 50 -and $timespacn.Minutes -lt 55

Answer 2

That's simple boolean algebra. You want to take action if neither of three conditions is true. That can be formulated like this:
!A ^ !B ^ !C # (not A) and (not B) and (not C)
The above can be transformed as follows ((!A ^ !B) ⇔ !(A v B)), since multiple negations in an expression tend to be ugly:
!(A v B v C) # not (A or B or C)
In your code that would look like this:
if (-not ((Test-Path ...) -or (Test-Path ...) -or ($timespan.Minutes ...))) {
...
}