Putting Mail back on track

The Apple iBook G3 Laptop is good enough, but Mail has been for the birds from the outset. I rely on Gmail to do the heavy lifting, but I like to read my mail on my native application. While I have many false starts in the past, recently Mail has fallen down on the job, its server is failing to pluck my mail from out where it is. When I send myself an email and send it by Mail, gmail has it in an instant. Mail has suddenly stopped stopped receiving my email. I've changed nothing prior to these failures. What's up? Where do I go from here?