On the RAM:
If the 80GB HDD is the stock drive, he has PCI version that can take a max of 4GB of RAM.
http://www.everymac.com/systems/apple/powermac_g5/specs/powermac_g5_1.8_dp_2.html
On the Superdrive:
It should be DVD-DL capable, since it came from stock with a Superdrive. Also, it is a 2004 model, so it is able to read/write both DVD-DL and DVD+DL (which G4/G5 until 2003 can't).
Maybe your media is incompatible or it was just this DVD that failed, try again with another (or was it the original Leopard DVD? Do you also have a black label on it? If grey you have a Leopard install from an Intel Mac.)
Go to "about this Mac" -> more info -> "burn media" (on the left). There you can see what media format is supported and what drive you have. When you search on Ebay use multible search terms like: multiwriter, multiburner or type in a certain model. This will get you a Drive for 1,-USD, because most people will search for "DVD-DL Drive". Auctions that do not have that in the title will not be found by them and will not get as much bids.
GSA-H12 is one (may have LG, Toshiba, HTL, Hitachi as a manufacturer label on it)
SH-S202 (by Samsung), I find it gets a bit hot and would prefer the LG one, though people say that LG drives do not take every media (i.e. every media type, but not every manufacturer).
You can also first search for "DVD DL IDE" or "DVD DL PATA" and look up model numbers and then use these for the search.
SATA-PCI-X cards
Though your's has PCI, it can take PCI-X (which means you will be able to have 62MB/s instead of 35MB/s throughput).
List see here
https://forums.macrumors.com/posts/18914237/
and
https://forums.macrumors.com/threads/1650568/ (list see #19 onwards, but read the info before and after that, too.)
If you like to flash:
https://forums.macrumors.com/threads/1690231/)_ (by harrymatic)