Q: Settings are all correct and still no incoming mail.

Setting provided by service provider have been checked and are all correct. Connection Doctor, in Mac Mail, says all connections are successful.  Incoming mail is received on my mobile device but not my desktop. I sent a test from myself to myself on my desktop and it only showed on my mobile device never came to my desktop even though it was sent from my desktop.  Service provider insists it's a Mac problem, since mail is coming and going on mobile.  It's even going out on desktop just not getting any incoming mail on my desktop.  Can you help?  Thanks