Is it possible to upgrade VPCEB42FM to play diablo 3

The only way to do that, is to get a Graphics Card.
To play D3, I suggest a 6770 or 6850 depending on what resolution you play on.

You cannot add/exchange gpus in your laptop

I believe that laptop has HD3000 GPU, is this true? Try using the settings this guy did:

http://www.youtube.com/watch?v=FNWMMOha0_w

If he IS using HD3000 graphics then the game will technically run on it.

i tried to adjust the decicated video memory in advanced settings

It is not clear, were you in the Bios? That is where you should be able to increase the dedicated video memory. It still may not be good enough to play D3, but it is a good try.

It says in this review
up to 1,696MB of shared Video memory

So try a 1Gb for the Video ram and 4 Gb for the system, that seems like a good match.

You might be able to adjust the video ram size in the bios. But I don't think the game will be playable.

Well guys I'm glad to tell you that I have exactly the same laptop: Sony Vaio VPCEB42FM and I'm playing Diablo since the day it was officially released! I must say that until a couple of week ago the game was slow even with all the options set to low or turned off, but after the last patch released by Blizzard the game is running 10x better. So I hope the guy that originally asked the question kept his laptop and is playing Diablo right now!!!  

P.S. - I never had to mess around with the default BIOS configuration for video memory allocation.