Email problem

We have both a desk top and a laptop in our home office and are connected to broadband ADSL. We have two email addresses, one for business and one personal. We can send and receive from both email addresses outside of our office, but cannot send and receive between our two computers. A window appears when we send an internal email, saying that we have encountered a problem and the email could not be sent. I have contacted my server numerous times without success. Any suggestions please???