retrieve old voicemail from broken iPhone

I have had many conversations with ATT tech support. It is different everytime I call ie:

The old iPhone 5c wouldn't turn screen on but gets warm. ATT store told me it was covered under insurance and to aquire a new replacement iPhone which is now a 5s. The new phone came next day, took it back to store, a guy unwrapped everything and installed the new sim into the new phone. Then they told me to take the new phone home and connect it to my iMac to retrieve the old data. I plugged it into my iMac and launched iTunes. That auto responded and asked if I wanted to back up from previous backup. I clicked yes. It retrieved photos, memos and videos but not voicemail. The voicemail icon was grayed out on the new phone. I called ATT and asked to have old voice mail put back on. They somehow activated voicemail and it is now on but no old is there. No one tried to take the old sim card out of the old phone or suggested it be put into the new phone. I still have the old iPhone 5c. Those voicemails have got to be somewhere! thanks, Marsha

Are my voicemails backed up on my hard drive? Thanks, Marsha