If a message you sent did not leave, read the recipient's address first. Then see whether your own box is full. A box that has used its quota stops accepting new mail and may stop sending as well.
MX and the name
Mail follows the MX line on the domain. If the nameserver opens the site and the MX line still points elsewhere, the site works and the mail drops. Read the line on the domain card. The recipient may also have filed your message under junk. Ask them to check a test message there.
Where the box opens
Work mail is on the mail shelf. The box is tied to the domain you bought. While the account is being prepared, the panel says so. When it opens, management is on the same card. The domain record is where the MX line lives.