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The best way to get your data off the hard disk is to get a USB to SATA adapter kit (example) to atach it to the other laptop running Windows Vista. It will then appear like an external hard disk and from here you can copy off the files you need to recover.
Once you have the files copied off it, I would then recommend running HDTune’s surface scan on it, which you can download here. This test will take a few hours and if it all shows green, you can place this hard disk back in the newer laptop and reinstall Windows 7 or run the recovery media (if you have these discs). If the HDTune surface scan shows any red dots, then the hard disk is defective, in which case you will need to get a replacement. As you mention you just bought the laptop, it should still be within warranty.