You can take the laptop hard drive out or your old laptop, buy an external casing for it and attach it to your new Laptop via a USB cable. The only potential problem with this is that when Vista finds the new hardware, it may not allow you access the files if there is problem with the drive. i.e. it may register the drive as "unhealthy".
(If you have any friends who are into PC maintenance, they may well have an IDE cable convertor, which would allow you attach a laptop hard drive to a desktop computer, so maybe check that option out too)
Another potential fix is to find out the manufacturer of the hard drive and download their hard disk utilities. Most manufacturers offer the utility in an .iso file format. Burn this .iso image to a CD from your new laptop.
If you place this CD into your old laptop and set the boot order to boot from the CD first, this will run the manufacturers diagnostic on the hard drive at startup.
I would give the latter option a try first, as that way is free!
Let me know how you get on.