rats123:
Hello and welcome to the Windows 7 forums. First I would like to endorse your idea of copy your files to an external drive for safe keeping, I might even suggest using a third party program like Acronis True Image or Ghost to create an image of your current OS, just so you have a strong fall back position.
Usually we see this type of issue as a product of either bad install media or else a failing or faltering DVD drive. So if your source media was a download from somewhere like MSDN or TechNet or somewhere else where you downloaded an ISO, you may find that if you re-burn the ISO using the slowest buring speed possible it may help. Also make sure to physically inspect the media itself for smudges, scratches, etc. Otherwise maybe swap the DVD drive temporarily to see if that might help.