Please tell me if my syntax is correct.

[Kristine May]

Are these correct:

"Your themes," said Ms. Buchanan, "will be due in class on September 7; late papers will lose one full grade."

What should I do when the computer says, "Sorry, try again?"

 

[Raymott]

Are these correct:

"Your themes," said Ms. Buchanan, "will be due in class on September 7; late papers will lose one full grade."

What should I do when the computer says, "Sorry, try again?"
What should I do when the computer says, "Sorry, try again"?

There might be some disagreement about this correction, but I think that putting the question mark inside the quotation marks is only correct if the quote is a question.

There was a thread a few months ago about a sentence which contains two questions, such as, "What should I do when the computer says, "Do you want to restart the computer?"
The consensus was that only one '?' was warranted, but I forget where it was supposed to come.

 

[Rover_KE]

What should I do when the computer says, "Sorry, try again"?

To me, the question mark must surely come outside the quotation marks.

Rover

 

[Raymott]

To me, the question mark must surely come outside the quotation marks.

Rover

Yes, but can you explain why this must surely be the case when, if we had a full stop playing the same role in a sentence, it comes inside the quotations marks?
The computer told me, "Sorry, try again."

I used to put the full stop outside the quotation marks on the grounds that the full stop indicated the end of the sentence, just as the question mark in the original sentence does.

 

[freezeframe]

Purdue OWL: Quotation Marks

Place a question mark or exclamation point within closing quotation marks if the punctuation applies to the quotation itself. Place the punctuation outside the closing quotation marks if the punctuation applies to the whole sentence.
Phillip asked, "Do you need this book?"
Does Dr. Lim always say to her students, "You must work harder"?

I'll trust that they know what they're talking about :-D
That website is recommended by my university's writing centers.