Your correct error 36 is a windows message saying a set file on the CD, or Dvd rom disk could not be read, or copied from.
Or could not extract source file from medium.
You could try giving the disk a good clean if it`s scratched, but sometimes it is down the the read and write laser of the drive being weak or worn out if the drive has been in the system you have for a good few years.
You could try a cleaning disk to see if it is just dirt, or dust on the reading laser of the drive to cure the error problem.
Short of that see if you can buy a disc replacement.
Or a download image of the game disk in Iso format to run the setup and installation of Nascar 2003.
do a Google search for theIsozone.
That`s as much as I can help you, since you own original licences by buying the game you are allowed to make a backup copy of the disk or game title for your own personal use.
If you get the Iso image of the cd, or dvd disk. then you can burn the disk image to a blank record able CD-R or DVD-R disk by using burning software Eeduranty ok.
Just found the Iso image file ! click on the link bellow.
http://www.theisozone.com/downloads/pc/windows-games/nascar-racing-2003/
Unzip with winzip, and burn the Iso image to a blank CD-R medium.