What could I do to help my parent who is depressed due to a broken hip?

Tough problem. My experience is that elderly patients become depressed after major injuries due to the loss of autonomy and decreased abilities. Helping them regain as much independence as possible is very important. Helping them return to their preinjury routine is also essential. Dinner with friends, a hair appointment, bingo, bridge club, sports activities, whatever they were doing before.
Talk to the doctor. Who is treating your parent's hip or call a mental health professional. Talk to your parent about his/her thoughts & feelings. Be empathic, not critical/judgmental. Provide or arrange help with tasks & encourage reasonable activities & interaction with supportive people. Help your parent feel useful while limited.