Annie, when you connect your NC to your BN cable and then connect the cable to its charger, does the "N" on the head of the cable light up? If not, the charger isn't delivering power to the cable.
You can try unseating the cable from the charger and connecting to a USB port on a computer. If the N lights up then, your NC will charge, albeit slowly.
If you're only able to charge your NC from a computer, if you take the NC + cable + charger to a local BN and show them that it isn't working, they ought to replace the charger or order you a replacement.
If the charger can get the N to light up and stay green, your charger is delivering current to the system but doing it slowly, or maybe not actually charging at all. If it lights up and goes from green to amber, the charger thinks it's working correctly and your NC is unable to charge. If it blinks on and off, or on/off/green/amber there's a bad connection within the cable.
There are a lot of reports of strange goings-on with the charging system.
My guess is that you may find that your NC needs to be replaced, and that it will be fastest to have a store employee verify that and start the replacement process rather than trying to get a replacement sent by explaining what's up over the phone.
Check your charger unit itself to be sure it's not getting too hot. A few people have reported that charging an NC with a very low battery can cause the charger to overheat, and some have actually had chargers melt.