How can I put my iPhone 4 in DFU Mode if the Home button is broken and it is turned off?
If the home button is non-functional, and the device requires a working home button to even power up, then it seems you're in a chicken-egg situation.  There is of course software that lets you remap some other button or UI action to correspond to the home button, but if you can't get the thing turned on you're out of that realm.

I suppose you could open it up and try shorting the contacts of the home button assembly, but once you're that far into it you may as well just replace the home button or the front panel.  The home button replacement part is only a few bucks, and the whole front panel is under $20 [in the US].