My other mailboxes are very full - is that an issue?
I can't say for sure, but the Mail applications for jaguar panther and tiger (less so) had problems when Mailboxes became too full.
Here is an Apple article on the subject that suggests creating more than one mailbox into smaller mailboxes using self defined categories for sorting.
http://support.apple.com/kb/TS1895
While it does not mention your earlier Mail version, i think it would still be relevant.
If you created new mailboxes and had no more than 100 MB in each one, I think then you could be confident that Mailbox size is not a factor.
It is only 16 messages that I can't delete. I can't even see the original emails - just the message regarding going online.
Emails are contained in database files called mbox, and the Mail application simply gives an appearance of items. Its index may be corrupted, showing you messages that are no longer stored.
If your Mailboxes are no longer too large, you could try and use Mail's rebuild function to re-order the index. Rebuild will be one of the choices from the menu. I can't say exactly where as I no longer use 10.2 but you will see it.
After that those emails may either no longer show up, or if they do, present themselves as deletable.