If your PC doesn't recognize the drive even for a moment while you reboot it.
And you didn't already have the rescue pack installed on jailbreak.
At this point the only options appear to be:
1: Take amazons offer, or call back and complain even more, trying to get a full replacements.
2: If you bought the kindle with a credit card, call your company and ask if they have an extended warranty program ( I know mine offer double warranty up to 2 years [ 6 months becomes 1 year, 1 year becomes 2 years and thats the max ] ), and see if you are in that timeframe.
3: Open the case of the kindle and perform electronic surgery.
3A Following the steps 1-4( in step 4, substep 1. ""Get into the diagnostics boot"") here
https://www.mobileread.com/forums/sh...d.php?t=267541
3B Buying a new logic board here or on ebay etc.
http://www.powerbookmedic.com/xcart1/home.php?cat=814
Keeping in mind that it could have been just bad timing, and something else may have broken while you did the update.
Here is a video of how you would have to take it apart:
http://www.powerbookmedic.com/manual.php?id=232 The 3 dots nest to the power cable at about 1:17 are where you would hook up the wires for Serial access.
The actual logic board replacement would be at 3:20, you wouldn't need the rest of the video.
Edit: Holy crap there are a lot of cables hooked into the logic board on the Voyage.