Pass those classes then apply and see how it goes. Not every school is going to deny you because you failed a prereq but then passed it at some point.
Something that can help you a lot is to take all of your non-nursing classes. Spend a year and completely knock all of that out. Even though you failed your anatomy and chemistry classes, getting those other classes out of the way actually shows them a different student than last time. Only retaking those two classes doesn't tell them much. Taking those 2 classes plus these other classes that you'll need for a BSN tells them that you're applying yourself and that you're serious, and that you're capable of finishing and passing the program. Just be aware of whatever school you're applying to's policy. Some only look at your highest grade, some only look at your first grade at that school, but some only look at your first grade anywhere. Make sure they're not going to still be looking at your prereqs as an F after you go back and pass them. Make sure you're only applying to schools that are going to look at the passing grade.
And if there's an interview or an essay where part of it is talking about your education, even though losing motivation isn't your fault, make it your fault. Own it and explain what changes you've made to keep that motivation. Show them that you have a plan on how to succeed.
Think of this like a job/business interview/advertisement. You need to sell yourself to them to be accepted into their program. Put as much on your side as you can.
And for your herniated disc, tons of nurses have gone through it and still work. It's going to depend your individual case. But as long as you're not a high risk of injury if you work safely, your doctor will probably clear you on your physical. Before going through all of this, you can even ask him about it at your next check-up visit, and he can give you a pretty good idea. Just don't be stupid. Use your aide. That's still their patient while you're in clinical (which is why I HATE schools that want us to stand in the hall and answer call lights, there's ALWAYS something to learn about your patient and their care and how what you're learning in your classes applies to it, and that's what you're there for, not to be an aide and give free labor). If the aide is busy, get another student or your teacher. Any lifting or moving that's an injury risk to you, get help. You should be doing that even if you don't already have a back injury.