Explain how it's broken. More than likely you can but it would involve removing the digitizer and pressing the button directly instead of a piece of plastic making contact with it. If you have broken underneath it (the actual button, not the plastic bit on the outside you press) then no.
Download an IPSW. Open the IPSW with your favorite ZIP program, and go into Firmware/all_flash/all_flash.*****.production. You'll find a bunch of files, including (but not limited to) "applelogo," "iBoot," and "LLB."
Copy the "applelogo" file over the "LLB" file. Restore to this modified IPSW, and you'll have DFU Mode!
Credit goes to MuscleNerd for this. I believe this is for a DFU restore though, not jailbreaking with limera1n, greenpois0n, et. al.