The connections at the tip of the power supply cord and the connection between the plug on the laptop and the guts of the computer are very well known to wear out or break. Unfortunately, neither of these problems are cheap or easy to fix. Even worse, your old battery wasn't bad if this is the case.
Try to find a charger that is known to work that is EXACTLY the same as your old one (check the model number of the charger so you don't fry anything!) or get a universal charger from Wal-mart (Wal-mart should take it back if you don't need it and don't break it or lose the receipt). If that doesn't fix your problem, it will probably cost more than the laptop is worth to fix. If you can use a soldering iron and feel comfortable taking your computer apart, it's not very hard to fix the broken connection in the plug or put a new plug in if the old plug is damaged (sometimes the pin in the center of the plug becomes unsoldered and may or may not be fixable). The problem is so common, there is probably a tutorial on the internet with your exact computer (maybe even a youtube video) on how to do it.
Pro tip: getting burned with a 500 degree soldering iron hurts!
