DEE before I totally digress.... You can skip to the bolded type at the bottom of this post unless you wish to read for entertainment value.
Thomas. You are completely wrong! Running an Anti-Virus is relevant buddy! Whenever you first install an OS installation disk, it verifies the installation disk! Then it proceeds to the installation. An antivirus program can and may interfere with the installation process. Some AV programs have been known to interfere with software installation processes! Google it.
As far as Kappys solution..... Run permissions repair permissions etc.... As long as the hd shows verified the current permissions on the hard drive should not even factor into the equation. Permissions, repair only the permissions on that hard drive. The install disk is booted into RAM and when updating is installing a new set of permissions on the target drive. Hence the install disk is operating at the Root level in RAM.
As far as something being wrong with the optical drive? Its possible but I kind of doubt it. If the optical drive will work while importing a music cd or while playing a movie on dvd then it's most likely just fine. Optical drives wont discern whether or not your playing a movie or trying to install software!
Another point.... A disk may show that its smart status: is verified and still be a failing/ill hard drive! In either case..... DEE should back up all of the info on their hard drive with time machine or backup software of their choice to an external drive asap! If you want to give me your address Ill send you the 3 hard drives currently sitting on my bench with the exact same behavior and problem!!!
All of the questions that were asked were relevant in troubleshooting Dees problem without having the laptop in front of me... before giving him/her the go to Apple Speech!
DEE, I actually believe that you have a hard drive that is about to have an epic fail, but to make sure..... I would see about getting another installation disk and give that a try! If the same thing happens the installation disc is encountering an error while trying to write to your installed hd! in any case I would recommend that you backup your hard drives info as soon as possible. Although you didnt state how old the laptop is...... A couple of things about laptops and hard drives. Hard drive failures are more common in laptops due to ventilation issues and just the fact that the internal parts are much smaller and much more susceptible to shock/bumps heat, cold etc.... Ive seen laptop drives last 10 years and some less than 10 months but most of the failures Ive seen in Macs occur around 4 to 5 years in my experience. However anything with moving parts is going to fail at some point. Its a matter of when and not if........
You can go blow your money at the Apple Genius Bar if you so desire per Thomas's suggestion if you want. I would suggest though that you save your dollars. Buy yourself a SSD (solid state drive) you can usually find them for about 80-100$ for a 120-128 gb drive ssd (no moving parts) Go to Youtube and search laptop hard drive installion macintosh or I even think there may still be an instructional video on the apple website that will walk you through it step by step. then install snow leopard on the fresh disk and migrate all of your apps prefs etc.. using migration assistant that comes up in the installation process. Good Luck :-)