Q: How to enter recovery mode when home button is broken and never connected to itunes

The only way is to use an application called Reibbot. See this link for details:http://www.technobezz.com/enter-recovery-mode-broken-home-button-iphone/

- Try another cable.

- Inspect the dock connector on the iPod for bent or missing contacts, foreign material, corroded contacts, broken, missing or cracked plastic.

- Try on another computer

Make sure that your device trusts the computer.

• Connect the computer or other device to your iOS device.
• If your iOS device is locked with a passcode, unlock it.
• Tap Trust.
  
• If you're about to sync the device with iTunes, click Accept.

Make sure that Apple mobile device support is installed ,

Windows 8

1. Move the cursor to the upper-right corner and click the magnifying glass.
2. Type Control Panel, and press Return.
3. Click "Uninstall a program."
4. Verify that Apple Mobile Device Support is visible in the list of currently installed programs.

If Apple Mobile Device Support isn't listed, remove iTunes, QuickTime, Apple Software Update, Apple Application Support, then reinstall iTunes.

• Reinstall iTunes for Windows XP
• Reinstall iTunes for Windows Vista, Windows 7, or Windows 8
  

If you reinstall iTunes, and Apple Mobile Device Support still isn't installed, you can resolve issues installing iTunes for Windows.

Windows Vista and Windows 7

1. Click Start.
2. Choose Control Panel.
3. Click "Uninstall a program" (if you're using Windows Vista's Classic View of the Control Panel, click "Programs and Features").
4. Verify that Apple Mobile Device Support is visible in the list of currently installed programs.

Windows XP

1. Click Start.
2. Choose Control Panel.
3. Open the "Add or Remove Programs" control panel and verify that Apple Mobile Device Support is visible in the list of currently installed programs.

For more help visit: iPhone, iPad, or iPod not recognized in iTunes for Windows - Apple Support