Goto the goldenhawk website and get the version 3.9A that is listed with widest compatability--it will ask if you want it to update ASPI for you--click yes:
http://www.goldenhawk.com/download.htm This also has some links for updating the ASPI manually, as well as a user guide.
It may actually be "ripping" the disc right, just not burning the backup properly. Make sure it is in DAO mode and none of the data is being manipulated/filtered/corrected in any way. Barring that, it may in fact be a media problem (unless you just got a weak laser). I have taken to burning my PSX's on 650MB Media, nothing certified higher than 24X. This will generally be a dense reflective layer, with minimal impedance from the dye layer. You may want to see if you can swap a few blanks with a friend if you can't get CDRWIN or CLONECD to work.
As for the CloneCD, it has been the best way for me to go--use EXACTLY as listed in the previous reply--make sure you read and burn as slow as the drive will go. Not absolutely necessary all the time, but considering you are already having trouble....better to be safe than sorry.
I would highly recommend CloneCD for the first try. I am using an older version simply because I don't like the newer skinned look. Even this older version burns them right on the first try 99% of the time. I don't want to discount CDRWIN, because it burns the few oddballs CloneCD doesn't get right. CloneCD just tends to be less difficult to use, and I can rip faster because it works better with my DVDROM as the reader (I don't have to swap the media, and each disc is ejected when it is through.) One nifty trick with the newer versions of CloneCD though is it will grab control of the drives BEFORE Winblows if you DON"T PUSH THE TRAY BACK IN--open the trays, lay the disc down, then click the Next/OK buttons and let CloneCD control the drive and it will step around some copy protection schemes better (supposedly--according to its author).
Good Luck!
Raist