Dialog with an ok and cancel button

I'd be interested in your analysis of the following sentence (from program documentation):

... dialog with an ok and cancel button... [correct]

Would be correct. However, why not:

... dialog with an ok and a cancel button... [correct]

And why not:

... dialog with an ok and cancel buttons... [incorrect]

And why not:

... dialog with an ok and a cancel buttons... [incorrect]

And why not:

... dialog with ok and cancel buttons... [correct]

Actually I would say that your first fragment, with an OK and Cancel button, is incorrect; it reads as if there is a single button that is labeled "OK and Cancel".

"With an OK and a Cancel button" correctly identified each individual button with its label. Because each button is identified separately, the use of singular is called for, even though the word "button" only appears once; this is a parallel construction in which the second occurrence of "button" is omitted.

For the same reason that "an OK and a Cancel button" is correct, the other variants "with an OK and a Cancel buttons" and "an OK and cancel buttons" are incorrect; the singular is called for, not the plural.

"with OK and Cancel buttons" is also correct because you are treating the buttons as a group, and lumping their labels together as a description of the group.

In the correct ones, you give exact or abbreviate representations of "an ok button and a cancel button"; it is also correct to emphasize the plurality of buttons, but then a/an are not appropriate.