The DVD might be bad.
Try to copy the contents of the DVD onto the hard drive and install without the DVD.
With the DVD in the drive.
First create a new folder to copy the files to.
Open My Computer
Open your C: drive
Create a new folder (name it something like Sims 3 Install)
Open My Computer.
Right-Click on the drive with the Sims 3 DVD in it and select Explore.
Hit Ctrl-A to select all files contained in the DVD.
Hit Ctrl-C to copy the files.
Now go to the new folder you made and hit Ctrl-V to paste the files into the folder.
After it is done transferring look for a file like setup.exe in the new folder.
If you're on vista or windows 7 right-click on the file and select Run as Administrator.
If you're on XP just double click.
Hopefully this works.