I suggest burning to or creating an image file, mounting that, and verifying your software is producing valid results. If the .ISO is able to be mounted and browsed, there is an issue between your computer and the disc burner.
Have you tried burning the disc at the lowest possible speed? Not all blank discs are rated for writing at all speeds.
Do your burners that you have tried have under-run protection and is it turned on in your burning software?
How have you verified that the data being copied from the original discs is being copied correctly? Commercial discs can have copy prevention mechanisms built into them. We can not help you circumvent anything of this nature here.
First things first though, you need to ensure you are extracting valid data from the original disc before you try writing it to a new one. You should be able to use a program such as Daemon-Tools Lite to extract an image of the original disc to a .ISO on your hard drive. At that point, you should be able to mount the .ISO image in Daemon-Tools Lite and use it as though it were the original disc. Until you can get this step to work, I wouldn't bother trying to go further with the process to burn a copy.
You haven't quite clarified yet whether the discs, after being written to, can be read by any system other than the computer presenting you the problem for which you're seeking help. Have you tried to read the discs in another system?
If the discs are being seen as blank, are you then able to re-run the process of burning data to the same disc? The reason I ask is, some disc burning software has what might be called a "simulation" mode where, it goes through the entire process, except doesn't actually burn the disc. It is used to verify that the process will complete successfully without wasting a blank disc if it fails. If your software is capable of simulating writing to the disc, make sure you are not doing that by mistake.
Also, make sure the disc or session is being closed after writing, unless you are specifically writing in a packet mode. While your XP system should read the disc fine even if it isn't closed, it's not guaranteed that it will, and non-PC devices may refuse to read the disc as well.