Can you connect to the PI Notifications Service locally? If you can, and you cannot remotely, then a block port seems to be the likely the issue. First thing I'd recommend doing is double checking the port on which the PI Notifications Service is listening. You can do this by running netstat -a. The default port is 5468.
You can then test the connection to the port using PowerShell on the remote client:
(New-Object Net.Sockets.TcpClient).Connect("<NotificationsMachine>", 5468)
If the port is opened and the connection still isn't working from PI System Explorer. The next likely culprit is a security issue. Are the two machines in the same domain? Can you access the service locally using the same account as remotely, etc ...
Hope this helps,