I just tried the AHT on my late 2011 15" MBP - everything checked out fine (your post just prompted me to make sure that it's working properly - I've nothing going wrong with my computer). You just have to keep that D key held down for a long, long time - don't release it until you see the AHT onscreen.
While you might be able to rule out bad RAM as a problem with your computer, you could also loop tests running the free Rember... and if you're having kernel panics, you could post a log on here to see if someone notices something unusual (I suspect you meant to say that you have no non-Apple kernel extensions?)/
To post a log of your most recent kernel panic, see http://support.apple.com/kb/HT2546?viewlocale=en_US.
The AHT depends on what OS your system shipped with, varajara, your system shipped with Snow Leopard, I'm guessing, so your AHT is on your applications DVD that shipped with it and will need to be inserted in to your optical drive to boot to the AHT. ssbarnea, since your MBP shipped with Snow Leopard, I'm guessing since it is an early 2011, you also need to insert the applicatiosn DVD that shipped with it.