You do need to remove that disk. Start by turning the laptop upside down and rest it on some cloth to prevent harming the screen. In what is now the lower right hand corner, you will see a hatch about 3" by 1½" held down by two screws to your right.
Undo those screws and remove the hatch. Below it is your hard disk and there may be more screws securing it. Remove those and gently ease the drive out of its position.
Buy a caddy or at least the cable needed to connect it to another machine and start by running Checkdisk in a command form. Use the syntax
chkdsk x: /r
where x is the drive letter given to your disk. Hit enter and let it run. The /r switch might be able fix any disk errors it finds. When it's finished, copy all your personal files into the PC you're working on.
You might wish to buy another disk for that laptop but in a time when manufacturers don't expect a laptop to last more than four years, spending money on a machine mmade to run Vista in 2006 may not be econimically viable.