Both accounts are configured identically. I haven't specifically tried the
second condition, but both machines can connect separately to the internet.
In fact, I downloaded mail from his ISP web account just to bes ure the
email passsword was correct. My intention is to leave the Gateway powered
down when I visit tomorrow and see if the Dell connects, which will be the
usual situation anyway.
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1.  It's not clear from your message whether both machines are configured to
use the same POP3 email account and password or not.  (That would be the
critical thing here.)

2.  It's also not clear whether, if you wait for a while and successfully
collect with the Dell, the failure moves to the Gateway.  Is that true?

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