[Trainer-Talk] reboot IPhone

[laotab ~]

Hi, I have an IPhone 5C.  the power button is broken.  I was getting a new app and listening to the tutorial and my battery died completely.  I cannot get it to charge again.  I tried 3 different outlets and 2 different cords and my laptop to charge it.  so I thought I would try to reboot it but my power button doesn't work.
I  had found a way to turn the phone off through accessories but with the phone dead I cant use that.
I never backed up my phone, of course.  And I have info on there and only there.  some the only contact I have with some people and no clue what their info is in my head.
Do I have any reasonable hope of getting my info back or rebooting it?
Also, I do not have a data plan.  I never used it as a phone.  I just used it for apps and text.
Thank you for your time.
Bridget, PA