Q: how can you put a ipod in recovery mode if the home button is broken and you dont know the passcode either?

You can't. Make an appointment at the Apple Genius Bar for service. If needed find an Apple Store - Find a Store - Apple.

If your iPod Touch, iPhone, or iPad is Broken

Apple does not fix iDevices. Instead, they exchange yours for a refurbished or new replacement depending upon the age of your device and refurbished inventories. On rare occasions when there are no longer refurbished units for your older model, they may replace it with the next newer model. You may take your device to an Apple retailer for help or you may call Customer Service and arrange to send your device to Apple: You can make an appointment at the Apple Retail Store - Genius Bar and take it in for service. You can also look for an Apple Store - Find a Store - Apple.

You will find respective repair costs in the appropriate link:

iPod Service Support and Costs

iPhone Service Support and Costs

iPad Service Support and Costs