My 4s charger port is broken so now my phone is dead and won`t turn on. I can`t retrieve any of my info such as photos, contacts, etc. What do I do so I don`t lose everything?

I have a 4s and last night my phone died because the battery was low but once I plugged in my charger, nothing happened. The night before I had problems with charging it because it wouldnt keep a solid connection so I just thought it was the charger itself but after everything I`ve tried such as other 4s chargers, the iHome docking station to try charging, and my laptop...nothing worked. I also tried cleaning out the charger port thinking it was full of dust but that was not the case either. So I came to the realization that my charger port has broken so now I am not able to get back into my phone and it is sitting here dead. I have lots of info and pictures on there that I would love not to lose because the last time I restored anything was back in November. Is there anything I can do to get into my phone and back-up all my info onto my laptop so I can transfer it onto a new 4s iPhone? Any help would be greatly appreciated. Thank you!