Connect to Sharepoint Online using powershelll credentials

Question

I would like to enumerate a Sharepoint Online list. The sample codes that I found are using the CSOM, which is fine, as the user who will run the script, won't have admin rights, but looks like I am missing something:

Function Get-ListItems([Microsoft.SharePoint.Client.ClientContext]$Context, [String]$ListTitle) {
    $list = $Context.Web.Lists.GetByTitle($ListTitle)
    $items = $list.GetItems([Microsoft.SharePoint.Client.CamlQuery]::CreateAllItemsQuery())  
    $Context.Load($items)
    $Context.ExecuteQuery()
    return $items 
}

#set environment
$targetsite = "https://sites/testsite"
$targetlist = "testlist"

$adminUsername = "admin@account"
$secureAdminPassword = Read-Host -AsSecureString "please enter password"

#ask the user to log in
$usercredentials = Get-Credential
#creating sharepiont credentials object

#$sharepointcred = New-Object Microsoft.SharePoint.Client.SharePointOnlineCredentials($usercredentials.UserName, $usercredentials.Password) 
$sharepointcred = New-Object Microsoft.SharePoint.Client.SharePointOnlineCredentials($adminUsername, $secureAdminPassword) 
#tried both


#create context
$Context = New-Object Microsoft.SharePoint.Client.ClientContext($targetsite)
#assign sharepoint credentials to context
$Context.Credentials = $sharepointcred 
#read list
$list = Get-ListItems -Context $Context -ListTitle $targetlist

$items = Get-ListItems -Context $context -ListTitle $targetlist
foreach($item in $items)
{
   Write-Host $item.Title
}

I tried to get the credentials different ways (visible int the code), but none of them seems to be working, I get the following error message:

Credential: [ERROR] Exception calling "ExecuteQuery" with "0" argument(s): "Unable to connect to the remote server"

The account I'm using has site collection admin rights on the site and the link I am using is valid. Can someone give me a hint where does this code go wrong?

UPDATE: This looks like a connectivity issue, because the code works for me when I run it at home. So, looks like something in the company network is blocking the connection. Can someone please post what ports shall be opened and which URL's should be allowed to make this working, so I can ask our network guys to do what's necessary?