The only way I got Hotmail to tell me I had mail was to set up a
text message alert when new mail arrives. It's under options, over to the right in your "in box" and I think it's under "more options", (scroll down to the bottom). Look for
mobile alerts for new messages and finish going through the wizard. It works 95% of the time. Hope this helps you. And IF you do have problems receiving alerts write tech support, they are good at resolving issues with hotmail glitches.
(any misspelled words is the keyboard's fault)