Computer doesn't start after installing new RAM

Please make sure you reseat the RAM sticks firmly (Until you hear two clicks, then push a little more.), and also try them in different DIMM slots. Make sure there is no dust in the way inside the DIMM or on the RAM itself.

If this does not work I would try them in another computer to attempt to find the real issue - the replacement sticks (unlikely, just like what psusi said), or the Motherboard. I did a little Googling, and it appears that psusi is right about BIOS updates. There are some and you can get them from the ASUS website for your laptop here. If you need instructions on installing the new BIOS update, don't hesitate to comment on my answer.

EDIT> I did not even notice that you changed from DDR2 to DDR3. Robotnik is right. Although, I am unsure how it's possible for you to mistakenly insert DDR3 into a DDR2 slot, as the RAM sticks have notches at different levels along the stick to prevent just that.

EDIT2> Nevermind, I have before seen computers that have the ability to support both DDR2 and DDR3. Awesome dude.

According to the product information page (which isn't always 100%) and the downloadable qualified compatible memory vendors and products... there is no compatible 1333 Kingston with that board. That doesn't mean it definitely wouldn't work, just lowers the probability.

According to the downloadable manual, there are two Kingston 1333 sticks listed, but one is 1gb and the other is 2gb... as far as compatible memory is concerned.

However, the manual says nothing at all about the board being able to use both DDR2 and DDR3 Ram. More importantly...

(image from Makeuseof.com)

... there is a physical difference between the two sticks, in the placement of the notch in the stick, and thus the placement of the pins that touch the contacts. Examining the top-down image of the board, you can clearly see where the notch would go in the Ram slots, so it isn't like there isn't a notch there. You can't physically put a DDR2 stick in either of those slots for the board you mention.

There are motherboards that will come with slots for both types of Ram... this is just not one of them.

If you are POSITIVE that the old Ram is DDR2, and you are POSITIVE that your system worked fine with it, then you must be mistaken about the motherboard model number.

But at the very least, there is no way that with the information you supplied that you were able to put DDR2 and DDR3 interchangeably in the same slots.