How to put iPhone in DFU mode without home button?

I recently got a broken iPhone to be fixed from a friend. The screen was cracked (already for a long time), the back panel was broken (also for a long time). But that wasn't main problem. The problem was that after the phone had frozen, she tried to reset it by pressing the home+sleep button for 10 seconds. The screen went black but didn't turn on again. Her Nokia-logic made her want to remove the battery for a few seconds and put it in again, and this was very easy since her back panel was broken. Of course this doesn't work with an iPhone so she tore the cable that connects the battery to the logic board. I replaced the battery but right now it won't turn on either. Normally I would try to put it in DFU mode but this doesn't work since the home button isn't working all the time anymore. I can't be sure what the problem is, whether the battery fix was enough or that the phone is really broken.

Do you have any ideas on how to put it in DFU mode without the home button or fixing this in another way? Thanks in advance!