Dell Laptop Adapter Problem?

[SmileyEH]

I've got a 2 year old Dell 9300 and for the past few weeks whenever I plug it in I get a message that the AC adapter isn't recognized by my system and the battery won't charge. So as a result my battery just slowly drains as it comes unplugged every so often. Now it's to the point that if the plug pulls out of the back my system turns off and I have to reboot-bleh it sucks. I've taped the little plug onto the back of my laptop and that seems to be working, but obviously a stopgap.

There is a cut in the cord b/w the laptop and the adaptor and some of the wire shielding is exposed, but it doesn't look that bad. Is that the cause or is a more serious issue at work that can't be fixed by just buying a new adapter (at $50 of course)? The problem actually stopped once last week and the battery was able to charge all the way back, but it came back the next day.

Thanks,