Problems with AC Adapter

I have been having some problems with external power supply on my Dell Inspiron 5100.

Even though the computer is connected to the AC adapter, and the adapter is connected to 220 volts, the computer is not taking power and running only off of batteries. Naturally, I also checked that the adapter's power indicator is on, and it is.

It seems that the computer takes some power from the AC adapter at times, but the power flow is not constant. The image on the computer is not in any way affected, but the brightness constantly keeps changing.

Needless to say, this is causing some difficulty in working.

I took the computer to an engineer to remedy the situation. He "pulsed" it, and everything was normal for two weeks. He also told me that the problem was in the computer itself.

But problems returned, and this time it appears to be in the adapter itself.

Just very recently, when the computer was working normally off the adapter, the latter started to get ***very*** hot -- as in you could not hold it for long for fear of literally burning your hands. As I write this posting, the situation is changed again; the AC adapter is plugged in and its power indicator is lit up, but it is absolutely cold to the touch.

I probably know what people are going to advise, but any information would be greatly appreciated.

CR