How to upgrade my Zen sub-theme so that navigation and most of the blocks are no longer missing?
The issue about How to upgrade Zen theme from 6.2 to 7.3 contains quite some info (and links to other resources) about such Zen upgrade. However it also includes these suggestions about possible alternatives to consider:


Something like "maybe you should just consider restarting from scratch".
Swap from the Zen theme to the Omega theme (by creating an Omega sub-theme from scratch).


For more in depth documentation, you might want to look at Upgrading 6.x themes to 7.x.

Based on the current (further edited) content of your question, these are some of the topics to be sorted out (at least):


Navigation:

The navigation items shown in D6, possibly correspond to your primary and/or secundary menus (though they may also come from some "custom" menu that got added). Check which technique was used to actually display that menu in D6. Possible options I can think of: (a) some block makes them show up or (b) some theme settings is turned on (enabled checkbox) to make them display. Depending on which option was used, try to find the corresponding D7 options to do the same there.
Blocks:

For any of the blocks shown in the D6 version, in which theme region were they displayed? Head over to the D7 version to verify where probably "most of these blocks" will be shown within the "disabled" list of blocks. For any such block you find, in the D7 version start experimenting with moving those disabled blocks to what you think will be the most appropriate region in D7.

Keep repeating this for each of your blocks that are missing (= iterative process). In doing so, little by little most (if not all) of your blocks should start showing up).


If sorting out the above topics appears to be too complicated and/or turns out to take too long, then I'd really consider going the route of either possible alternatives mentioned above, because creating a "sub-theme" from the most recent Zen or Omega theme might simplify further maintenance of your "custom" theme also.