what exactly do you mean by volume down broken, as in literally broken??
Do you have sdk on your computer, if you don't put it on your computer and I will tell you how to use ADB commands to reboot and do a miriad of other things. go toward the bottom of the page and look for "SDK Tools Only" and download the package for your computer. Sending you a PM so you can get a hold of me on hangouts
If you don't want to do that (and you really should) titanium backup has a reboot to recovery feature on it, open menu and it's in there
https://developer.android.com/sdk/index.html