Q: iPod Classic Won't show up in iTunes

The latest version of iTunes (12.5.1) should run under OS X 10.9.5.  Is there a reason you are using an older version of iTunes.  An iPod classic should work with even older versions of iTunes, but there may be an issue with the specific version you have (corrected in later version).

If updating does not help (or you don't want to update iTunes), since iPod is recognized by the system, it appears to have a data connection.  Try putting iPod into Disk Mode.

How to put your iPod into disk mode - Apple Support

Before connecting iPod, shut down (power off) the MacBook and disconnect all USB devices.  Connect MacBook's power adapter (so it's not running on battery power).  Start up MacBook, run iTunes, and connect iPod (in Disk Mode) to a direct USB port on MacBook, by itself.

If iTunes picks it up, it should prompt you to do a Restore with a message about "recovery."  This erases the iPod, so if you're OK with that (because the iPod's content is in your iTunes library), do the Restore.  Hopefully, the iPod appears in iTunes (normally) after the Restore.

So, is the version of iTunes now 12.5.1? 

My computer recognizes the iPod but not iTunes.

Does that mean the iPod's disk appears on MacBook's Desktop (or in Finder window's sidebar) as a storage volume, when you connect it?  Or are you seeing it recognized somewhere else?

When you connect iPod (in normal mode), watch the iPod's screen.  Does it initially say "Connected" or "Do not disconnect" or give other indication of a data connection?  Or does it only show the battery charging symbol?  Or does it not react at all to being connected?

You won't see anything on the iPod when viewed using Finder.  The data iTunes syncs to it is hidden, when viewed using a regular file manager.

It's good that your iPod appears in on the Mac's desktop.  That means it has a good data connection, which is halfway there.  When you run iTunes with iPod connected, you don't see iPod's device button?  Here's a screenshot of my iTunes window, upper-left corner, with iPod's device button circled in red

If you see this button, click it to show iPod's Summary settings screen in iTunes window.

Start up the Mac in Safe Mode (start up with Shift key held down)

Try safe mode if your Mac doesn't finish starting up - Apple Support

Run iTunes and connect iPod.  Is there any difference?

OR, do you have access to, or know someone with, another recent Mac?  If so, try connecting the iPod there to see if there's any difference for iTunes recognition.

Another thing is your current version of OS X, which is several major releases old, and the oldest one that can run the current version of iTunes.  Select About This Mac from the Apple menu.  What does it say there about your MacBook model?

If your iPod was previously used with a Mac, it may be formatted for Mac.  If so, you'll need to do a Restore on it to get it formatted for Windows.  It may be formatted for Windows now, because a Mac can use a Windows-formatted iPod, but a Windows PC cannot use a Mac-formmated iPod.

Either way, since you were having problem using it with the Mac, you may want to do a Restore using iTunes on the PC.  If you connect the iPod in Disk Mode, iTunes should prompt you to do a Restore, with a message about "recovery."  After the Restore completes, you get a message inviting your to "Get Started" with your iPod (like it's brand new).