How do I put my iTouch in recovery mode with no home button?

4th gen iTouch (might be in iOS 6.1.3) - Broken home button - cannot connect to iTunes/computer because of the passcode lock - I forgot the password

I looked at similar posts in the apple community that helped me, but there are a few problems. I need to put my iPod Touch in recovery mode, but I can't do that without the home button. I downloaded a couple of desktop apps for this situation (RecBoot, TinyUmbrella) but they won't work either because my iPod cannot be recognized by my computer, and my iPod cannot be recognized because I forgot the password!

My main goal is to get rid of the passcode lock.

I feel like I'm out of options, but hopefully someone might have an answer. (or that Apple Support user with the cat profile picture)