William, I haven't used an external DVD RW but I guess it must operate on the same basis as the ones I have fitted to my PC.
I assume that you have appropriate software for this DVD RW ie Sonic or Nero?
You may be having trouble because you can't use the Windows XP program for DVDs only CDs....if you want to explain your difficulties, I will try to assist.
I am suggesting you copy your files to disc, because if you have trouble with your new PC for any reason, and you have given the other one away ( I assume you may 'wipe' your files from it) you will be stuffed without a back up ie a disc.
I think you should select the files you want to keep copy them all into a single large folder (or two or three large folders), make a note of the folder / file size when you have done this to make sure they don't exceed the capacity of a DVD.
You can usually check the folder size by hovering the mouse cursor on it, but to be sure you can 'right click' it and then click 'Properties'.
If you exceed the disc capacity you will have to juggle your files around or make another folder to reduce the sizes.
If we can get your DVD RW to successfully copy to disc, then you have won....
all you will need to do with the new PC, once you have it up and running, is to load the DVD, copy it to an appropriate folder and then redistribute your files accordingly.
Keeping programs is another issue....any of these to be kept?
I will be going off in a while, so if you haven't replied or understood etc etc, I'll pick up in the morning or you can send me a PM and carry on by email. Up to you.
Al.