10.2 would be OS X Jaguar ... a true classic!
The issue you're encountering with the DVD might not be due to the age of the Mac itself, but rather compatibility with the DVD format. Power Mac G4 models typically support DVD-ROM, DVD-R, DVD-RW, and CD formats, but older models might not support newer DVD formats like DVD+R or DVD+RW.
That DVD Video you found may not be compatible with this G4. If it's a newer format that the Mac doesn't support, you might need to find a different DVD or consider transferring the contents to a format that's compatible. Additionally, you can still check if the DVD drive is functioning properly by trying different discs. If the drive seems to be working fine with other discs but not with this particular one, it's likely an issue with the disc's compatibility.
If compatibility isn't the issue, there might be a problem with the DVD drive itself. You can try cleaning the drive's lens using a lens cleaning kit or compressed air. I know they still sell CD/DVD "lens cleaning" discs. Here's an example of them that you can get from Amazon.