You should take a look at the InCD troubleshooting guide for XP
http://www.cdrlabs.com/phpBB/viewtopic.php?p=43689#43689 and the related (a bit fuller) version for W2K
http://club.cdfreaks.com/showthread.php?s=&threadid=60163 My first bet would be for driver conflicts on your work box, but media quality can't be excluded at this stage.
So first of all, you should test better media (4x-10x or 4x-12x from manufacturers such as Verbatim, since Lite-On and Memorex CD-RW are poor), and eject via the InCD icon (not the burner's button).
In general, describe your tests in detail, since I can only guess that "files disappear" means Explorer no longer lists them, and I don't know what "destroyed CDRWs" look like. BTW, did you try to recover them by running Full Erase in Nero?
Since two boxes are involved, each with two burners, for simplicity you should test the Lite-On burners only; further, each box must first be troubleshooted on its own. Here are some basic questions.
Are you using classical UDF 1.5 or CD-MRW (Mt. Rainier) formatting?
Do you have Autorun on for your burners?
Did you install EasyWriteReader on your boxes?
Does InCD operate correctly on each box? E.g., do you get the InCD mounted message after formatting, and after ejecting and reinserting a formatted disc? Are the files you copied to a disc visible in Explorer after reinsertion?
Except for Nero and InCD, did you use other burning programs or plugins (e.g., from WMP, WinAmp, etc) on your boxes?
To haunt for conflicting drivers, run the dir commands described in the first link above and post the results here. Moreover, extract the initial system information section and the final "Existing Drivers" section from the Nero log file and post it. What does Nero InfoTool say about your ASPI layers?