Can Chargers Go Bad?

I've been having problems with my mini's battery - no full charge, drains and then suddenly revives, takes more than a day for a full charge, etc. Then this morning, it wouldn't charge from the wall charger. Thought the battery was finally dead but tried the usb cable - it immediately began charging. But it still won't recognize the wall charger.

Is it time to ditch the charger or should I swap out the battery AND the charger?

Thanks!