Did they tell you that you must first reboot your PC and modem before the problem could be resolved?

No, but I was expecting them to. Towards the end he started mumbling that they don't support "3rd party" mail programs. I took it to mean if you have a Mac you are on your own.
The funny thing was, his technical knowledge sounded OK until you challenged some of his statements. For example, when attempting to connect to the mail server directly, I would get slightly different responses, eg.
421 nschwcmgw03p BigPond Outbound Connection refused. OB113
421 nschwcmgw04p BigPond Outbound Connection refused. OB113
421 nschwcmgw05p BigPond Outbound Connection refused. OB113
421 nschwcmgw07p BigPond Outbound Connection refused. OB113
421 nschwcmgw08p BigPond Outbound Connection refused. OB113
421 nschwcmgw09p BigPond Outbound Connection refused. OB113
That looked like a server name to me so I asked "How many mail servers do you have?"
He replied: "two". Sounded a bit strange. For all of Australia, all mail is handled by just two servers?
He goes on, "Yes we have port 25 and port 587. Two servers."
Me: "Ah that is the port for the incoming connections, that isn't two servers."
Him: "No, two servers: 25 and 587."
Me: "Each server has its own IP address. So how many actual servers do you have?"
Him: "Just two, sir. One on 25 and one on 587, like I said."
Me: "How do you account for all those different names in the 'connection refused' message?"
Him: "Let's delete your email account, and re-add it. Make sure you follow my instructions exactly."
Me: <sigh>