If smart disk utility doesn't give you anything, load up an image of windows and run chkdisk. This will mark any bad sectors as unusable and you can continue to install Zorin safely.
If there are bad sectors, you will want to start shopping for a new drive. It could be two years from now, but eventually it will not boot anymore. You may still be able to hook it up as a child and copy things off. Backup regularly and expect it to die.