I don't have access to the Sharepoint server and can't use remoting, and therefore don't have access to Microsoft.Sharepoint.Powershell
which contains the SharePoint commandlets.
I also can't use 3rd party libraries which means I only have access to built in Powershell commandlets, or any .NET class.
How can I access a Sharepoint list using only built in Powershell commandlets or .NET classes?
Well if you are using SharePoint 2010 and you don't have access to the server itself and must interact with it remotely you have essentially three options: https://msdn.microsoft.com/en-us/library/office/hh313619(v=office.14).aspx
You can use:
FWIW, the CSOM libraries use the REST endpoints under the covers.