This article is written about a specific model, but the method is worth trying for any laptop power supply!
So I got the eeepc 1005ha-p, which is the model with bluetooth and the higher capacity battery and the higher quality camera. After a little tweaking, I got everything working with eeebuntu (installed the kubuntu-desktop packages so I'd have a usable desktop). This little bugger really impressed me, even though I had only had it for about a week.. I was very excited to take it on a trip to Indianapolis, when out of nowhere the power supply stopped working. It has a little blue light on it that shows when it has power. I tried changing power outlets, and even tested the AC portion of the cable with a voltmeter to make sure it was geting juice, and everything looked fine. I searched the web sites of all the electronics chains to see if there were any third party replacements for it, but it looked like it was just too new. I couldn't believe it, its only a 2.1 amp supply, its not like it gets hot and burns out or anything.. and it died when it wasn't even plugged into the netbook.
That sounded familiar. A long time ago, when laptops were new, I had a power adapter that would overheat some internal component if it was left plugged in without a load on it. It was really silly, but the "cure" was to stick it in the freezer for 10 minutes or so and try again. I figured it was worth a try, and if it didn't work I was going laptop-free on my trip.
Ten minutes later, I had a working charger again. Now, when I'm not plugged into the charger, I unplug it.
Evidently, this charger is used on several other newer eeepc models, like the 1008, which is also a Seashell model. If your power supply seems to have given up the ghost, try this method before you buy a new one. Mine has been fine for the last month at this point.