In order to use any version of Adobe Photoshop, you will need to enter your product key to prove that you actually paid for the software (the product key is referred to as a "serial number" by Adobe). The product key is also necessary if you wish to upgrade the software. Fortunately, there are several ways to find your Photoshop CS3 key.
Check the packaging for your product. If you purchased a hard copy of Adobe Photoshop CS3, check the back cover of the disk case. The serial number is also printed on a sticker on the sleeve containing the disk, if it didn't come in a case.
Check your Adobe account for the number, if you registered or purchased your product online. Go to Adobe.com. Log in and select "View Order History." From there, choose "Your Downloads." On the Downloads page, look near the Downloads link for the serial number.
Locate the email received from Adobe when you purchased the product, if you bought it online as a download. If the email isn't in your inbox, check your spam folder or see if you saved the email as a document on your computer.
Open Adobe Photoshop CS3 and click "Help." Then select "System Info." The serial number should be listed right beneath "Image Cache Levels."
Download and install a free product key finder if you still can't find it using the methods suggested by Adobe. Product key finders search your computer's registry for the serial number. Free product key finders include Product Key Finder and Win KeyFinder (see links by Resources).
If you still can't find the number and you purchased the product legitimately, contact Adobe Support for more help on the matter.