Burnt out graphics card / data removal

Hi, i have a sony-vaio laptop with two separated hard-drives. recently it the graphics card burnt out (i think) and now the laptop fails to boot up. i took it to a few computer reapir centres and they told me it is pointless to repair due to the cost and effort.

I would REALLY like my data from it, so i was wondering how i could potentially fix the graphics card?? OR how i could get the data on the unbootable laptop elsewhere, say onto another laptop. please help, thanks.

also the hard-drive is enclosed in the laptop and i dont think it is removable.