Please provided more info:
When you say, "remotely connected laptop," do mean a laptop connected to a different local network, say at a local coffee shop or at your work? (If the answer to this is yes, it likely means your IP address might be in an RBL
. You'll need to work with your ISP to clear that up.)
What mail clients have you tested on the laptop and desktop?
If you have webmail interface for your mail account, does it work on the laptop? On the desktop?
Does the mail get sent and bounced back from the remote smtp server or does it never get sent in the first place?
Do the mail headers of the returned mail contain any bounce messages? (Different email clients have different methods for viewing the headers.)
Edit: Don't expect bounce messages in the headers to be very helpful. Sometimes, all they provide is hints about the next step in the hunt.