Moving from Office 2003 to Office 2013 - code no longer works

Some years ago I wrote some VBA code to send emails from within Excel for a school application.
The spreadsheet automated the cover and invigilation process.
I then retired from teaching and the school continued to use the spreadsheet.
They have now upgraded to Office 2013 and have asked me for help because the emailing code no longer works.
Unfortunately I wrote the code 10 years ago and have not kept up with it since, so I am not sure how to proceed.

It would appear that the process to create an Outlook session in Office 2013 has changed.
Could someone kindly point me in the right direction?

The Outlook session code follows:

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Thanks for the reply. Unfortunately I do not yet know what the error messages are. The people at the school contacted me yesterday and did not provide much detail. I had password protected some macros and the passwords they were trying did not work. I suspect someone may have 'fiddled' with them over the years that I have been away.
I sent them a copy of the spreadsheet with passwords that I knew worked, and I am awaiting a response. I will investigate the link you sent. Much obliged.

Jeff, reading that link refreshed my memory. I now recollect setting the library reference when I first wrote the VBA. If they have not selected the Office 13 Object libraries that would explain why the macro fails.
Fingers crossed - I think you may have solved the problem!

I think the one you want is "Microsoft Outlook 15.0 Object Library." The internal version numbers are different than the marketing version; Office 13 is version 15.0.