Those test failures do indicate that the hard drive is failing. You should back up all your important personal data, photos, music, etc to an external hard drive or CD/DVDs, you don't actually need a back up program to do this, just copy all the files you don't want to loose. All software, including Windows, will have to be re-installed when you get a new hard drive.
You could use a disc cloning program to copy the entire hard drive to the new one, but with Read Errors having been detected there is a risk of data corruption so I would recommend starting from scratch with the replacement hard drive.
You could use a disc cloning program to copy the entire hard drive to the new one, but with Read Errors having been detected there is a risk of data corruption so I would recommend starting from scratch with the replacement hard drive.