Questions / Things to check:
1. Are there any lights on either the cord itself (specifically the power block that regulates the power) and are there any lights on the laptop that illuminate with the power cord plugged in but the battery removed. Also try unplugging the links of the power cord and plugging them back in together again once for good measure.
2. Do you, or have you smelled anything funny coming from the laptop, specifically close to a vent or where the power plug goes in? If it burned out or had a fault you would smell Ozone or a light burning smell.
3. Check the area where the plug goes into the laptop. Visibly check to see if any prong(s) are moved to the side or anything appears out of order. Also check by plugging the adapter in, it should be snug and fit just right. If it is at all loose or wobbly, it may have added to the problem.
4. You could try getting a hold of a universal power adapter and giving it a try. Most retailers that work on PCs usually have one behind the counter for laptops, you may wan to see if they can let you use it just for a quick test.
I'm honestly more in agreement with Bradumd
, I think either there is a problem with the motherboard inside the laptop, or there is a problem with the power flow from the adapter to the battery, and adapter to the laptop itself. Not at all an easy or quick fix. But it can be fixed.