Articles Not Appearing In Sequence

When I create a new article then it always appears at the top of the page rather than in the order I have put it. Can you offer any advice?

Did you set article ordering in global article options. When you go to article manager then click "options" icon , you have tab for article options. Also there is same option on menu item level. So make sure defult order is set on all places.

Settings are as follows:-
Article Manager Options >>> Shared Options

Category Order - No Order
Article Order- Ordering
Date for Ordering - Published
Pagination - Auto
Pagination Results - Show

The 4 published articles which are listed are:-
Welcome (1)
Downloads (2)
Donations (3)
Contact Us (4)

However on the actual site they are displayed in the following order
3
2
1
4

Even though they are listed in the correct order in Article Manager

And in menu item under "Blog Layout Options" (right panel) you also have "Article Order" parameter

Do you mean "Blog / Featured Layouts"?
That is set to:-

These settings apply for blog or featured layouts unless they are changed for a specific menu item.

# Leading Articles 1
# Intro Articles 4
# Columns 2
# Links 4
Multi Column Order Down Across

Ok, but also you have "Article Order" parameter there