I have absolutely same problem (I posted my details in a wrong category by mistake, in fact I have a G5):
http://discussions.apple.com/message.jspa?messageID=4229521#4229521
What makes my situation worse, I actually came to an Apple store and they suggested to replace the drive(:_.
It becomes almost 100% clear that:
a) G5 (at least with SONY DVD RW DW-U21A ) can only burn certain types of DVDs, likely old ones. (In my case, the only successful try was with the Apple(!!!) DVD-R manufactured in Taiwan in 2004. Just yesterday, I bought a box of Sony DVD-R, hoping that Sony drive must burn Sony disks. No luck there either.
b) It has started happening after (what? I personally believe, after one of auto-updates). All of us here seem to be able to burn DVDs in the past.
c) Apparently, Apple doesn't care to comment or acknowledge there's a problem.
Finally,
d) I was invited to :
"Tell us about your experience at the Apple Store. Visit
www.apple.com/feedback/retail.html".
However this site doesn't work (with the promise or re-opening in March:-)).
I think we must do something about that.
Power Mac G5; Dual 1.8; 2G DDR; SONY DVD RW DW-U21A Mac OS X (10.3.9)