Dell Inspiron 1520 Battery Won't Charge

My battery for my Dell Inspiron 1520 will not charge. My AC Adapter is fine and powering the laptop, but the battery, that IS connected (I have taken it out and put it back in) has remained at 0% for the last few days. I recently posted this complaint in another thread, but after reading so many similar complaints, I realized I should make my own. I now understand the warranty for a battery is 1 year, but I have a few very frustrating issues with this:
First, I purchased the 3 year extended warranty assuming all parts would be included- this is, to me, common sense regardless of whether the battery is considered a consumable product or not.
Second, I have had this laptop for only 13 and half months! This feels terrible- a product which I have had a 1 year warranty for (which I assumed was 3 years) has died a month and a half after it would have been freely replaced. I am a poor college student, and this laptop was expensive enough when I bought it!
And last, I have rarely used this battery! I have taken it on only 4-5 car trips, and I can not even recall the last time (minus right now) the battery went to 0%, as I ALWAYS have it plugged in; in fact, I would surmise that if I were to use my battery as much as the average user (certainly more than me) then this battery probably would have died long ago when it was actually under its separate and special warranty! Should I be penalized for rarely using what appears to be a bad product? After all, minus the aforementioned car rides, the only time I've really used the battery is when the charger has accidentally been unplugged! As I responded in the other thread, if a product is going to be considered consumable, perhaps it should do its job more than a handful of times before malfunctioning!
I do hope this is a different problem altogether and not my battery, and if so, I apologize, but, after reading many similar situations, the only problem here seems to be with the battery, and this is very frustrating!