Why won't my old iPod (4th gen) sync with iTunes 11.1.5?

Question

My 40GB 4th generation iPod won't sync automatically or manually when I connect it (via iPod dock) to my Mac Mini running OSX 10.8.5 and iTunes 11.1.5.
The iPod shows up in the iTunes side bar, but that's the extent of the interaction between the two. Even dragging selected songs to playlists in the sidebar won't work. Is this just an age-related incompatability issue for which there's no fix, or is there a solution? Thanks.

Answer 1

If those options are grayed out, that probably means the Sync Music checkbox on the iPod's Music screen is not checked.  Then, your iPod is set to sync manually.  Check the iPod's Summary screen in iTunes to see if Manually manage music is checked.  If it is, the iPod is maintained manually, NOT automatically when it is connect or when you click the Sync button.
I wanted to select the latter so that just the songs I checked off in my iTunes library (those added since the last time I synced the iPod) were copied over.
Automatic syncing does not work that way.  When you set up the iPod's Music screen (and Apply), it syncs based on what you select on that screen (the songs that are part of the selected playlists, artists, albums and/or genres).  It does not add songs to what is already on the iPod, based on what is checked or not check in your iTunes library.
If you want to add songs to what is already on the iPod, and the iPod is currently set to Manually manage music, this is how to add (and remove) songs.
To Add songs manually...  Show a list of songs in the iTunes window.  For example, you can click on Music under LIBRARY to show your main iTunes music library list.  Select a song that you want on the iPod, and drag it to the iPod in the sidebar.  You can select more than one song at a time when you do this.  Alternately, select the song(s), right-click on the selection, and choose the command to Add to Playlist -> [name of your iPod].
To Remove songs manually...  In the sidebar, click on the small triangle to the LEFT of the iPod's name, to drop down the iPod's content list, indented below the iPod.  Click on Music there.  To the right, the iPod's song list is shown.  Select the song you want to remove from the iPod, and press Delete on the keyboard.  You can do this with more than one song selected.
There's nothing on the iPod that's not currently in my iTunes library, but I'd prefer not having to do a complete resync.
So, if you want to set up automatic syncing, you can check the box for Sync Music on the iPod's Music screen.  If 40GB is enough to hold your entire iTunes music library, you can choose to sync Entire music library.  Then, "everything" (that is music) syncs to the iPod.  Going forward, any changes to your iTunes music library automatically syncs to the iPod (the next time it is connected or you click Sync if already connected).
Otherwise, you can choose to sync Selected playlists, artists, albums, and genres.  A good way to set this up is to create new playlists in your iTunes library with ALL (and only) the songs you want on the iPod (or you can use existing playlists).  Back on the iPod Music screen, select those playlists under Playlists.  Going forward, to update the iPod, just update those playlists (add/remove songs) in your iTunes library.  So, if you have new songs, add them to one of those playlists.  iTunes automatically updates the iPod with the same changes (the next time it is connected or you click Sync if already connected).
When you click Apply, the existing content on the iPod is replaced by the content selected on the iPod's Music screen.  Going forward, iTunes is responsible for automatically keeping the iPod "in sync" with your iTunes library, based on now the iPod's Music screen is set up. 
To me, setting up and using automatic syncing is the most convenient and elegant way.