Inspiron 1720 AC Adaptor Cut Out And Now My Laptop's Dead!

I was running my laptop off the battery yesterday when I got the warning pop-up saying that the battery was about to go flat, and that I should switch to AC power. I plugged in the mains adaptor, and the computer ran on mains power for about 30 seconds when I heard a “pop” type noise coming from the area where the power adaptor plugs into the computer. The computer immediately switched back to battery power, but kept on working. I then got the “battery critical” warning, so I saved the data and turned the computer off in the conventional way.

I then noticed that the light on the power adaptor was off, and figured the extension lead I had the the adaptor plugged into must have blown a fuse. I plugged the adaptor into a power socket in another room, and it seemed to be working, so I plugged it into the computer again. The blue light on the side of the laptop came on, so left it to recharge the battery. When I came back to the laptop an hour or so later the light on the computer had gone out, so I figured the battery had been recharged.

When I went to turn on the computer this morning, it was completely dead. Thinking the battery must still be flat for some reason, I tried to run the laptop off AC power, but when I connect the adaptor to the computer, the adaptor stops working and the green light goes out. If I unplug the adaptor from both the wall socket and the computer, and then plug the adaptor into the mains again, the adaptor appears to work (the green light comes on and I have tested the output with a multimeter), but when I plug it into the laptop it cuts out again. Thinking the adaptor might be at fault I got hold of another one, but get exactly the same result when I use it. Any idea what the problem might be?