Thanks so much for your patience.
My apologies for the later reply. I was pulled for the day for an unexpected family emergency and had not been able to come back on JustAnswer.com (Mac) to assist you until now.
I have reviewed the screenshots you uploaded and appreciate you taking the time
to do so. Unfortunately, you have a text book setup in regards XXXXX XXXXX SMTP settings
For Outgoing Mail Server address for Sky. But that is not the unfortunate news.
What is, is the fact that there appears to be an issue with the incoming server ports being blocked from Sky and it is affecting a good amount of Sky customers. So it is not your Mac or your settings.
In my effort to get an answer for you, I did find this link which will allow you to check your email settings for Mac OS X Mail for Leopard.Sky Email Setup and Settings
After you check your settings from Sky's website and find that your settings for your Outgoing Mail Server address is correct, despite your Sky working on your Dell, you will need to contact Sky's Support.
I stress this because you would need to contact the ISP, to find if there are any existing or known issues occurring with the outgoing mail server for Mac using Mac OS X Mail. There are a number of Mac Users with Sky services, that are having the same issue you are: "Incoming email works great, but cannot send out emails"
Finally, to support what I am explaining about your Outgoing Mail server address issue, here is one of a number of links of customer's experiencing this same issue
Here is one such link:Sky User Forum
(Incoming Not Outgoing)
I hope this information can shed some light of what the issue is, from Mac level - the ISP side.
If you have more questions on this subject, please feel free to reply back to this post once again.
Thanks again so much for your patience and for trusting me to work hard for a resolution for you.