Q: My iPod won't connect.

Does your old iPod (with non-working buttons) still connect to iTunes, using the same USB docking cable?

When you connect 5th gen iPod, watch its screen (as you connect it).  Does it initially say "Do not disconnect" or "Connected" 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?

Also, is your computer running iTunes a Mac or Windows PC?  If Windows, what release?

If you get that message on computer, I think iPod has a data connection with computer.  You can try the troubleshooting advice in this document, including the more technical suggestions starting where it says If you use a Windows PC

If iTunes doesn't recognize your iPhone, iPad, or iPod - Apple Support

In your case, some of it may not apply, because you can successfully connect your other Apple devices to the same computer using the same docking cable.

Try putting iPod into Disk Mode

How to put your iPod into disk mode - Apple Support

Shut down (power off) the computer and disconnect all USB devices (except for USB keyboard/mouse if used).  If your computer is a laptop, connect its power adapter (so it's not running on battery power).  Start up computer, run iTunes, and connect iPod (in Disk Mode) to a direct USB port, by itself.

If iTunes picks up iPod, it prompts you to do a Restore with a message about "recovery."  This erases iPod and sets it to default "factory" condition.  If that's OK, do the Restore.  After it completes, iTunes invites you to "Get Started" with your iPod, like it's new.

If iPod is still not recognized, even in Disk Mode, please post back with any additional details.

If iPod's screen always says "OK to disconnect" when you connect it in Disk Mode, there is probably no data connection between iPod and computer.  The iPod's dock connector may be faulty, and not connecting for data, although it may connect for power to charge battery.  This is possible, because that "30-pin" dock connector has separate pins for power and data.

You've already ruled out a problem with docking cable, computer's USB port, and iTunes installation, because your other devices don't have this problem.  Normally, I would also suggest completely uninstalling iTunes and related software components, as described in this document

Remove and reinstall iTunes and related software components for Windows 7 and later - Apple Support

and downloading/installing the latest version of iTunes here

http://www.apple.com/itunes/

You can try it, but since your other devices do not have this problem and connect fine with iTunes, the cause is likely to be on the 5th gen iPod, not with iTunes.

One more thing...  You can visually check iPod's dock connector, by shining a flashlight into it.  Look for any obvious debris, dust accumulation, corrosion, or damage that may be blocking a proper connection.