What condition is your CD in? I don't recall ever having any trouble copying UT, or ever needing a no-cd. I don't believe there's any protection.
Hopefully, you have a CD-burner w/ some burn-proof technology.. try making an image of the cd on your HD and mounting it w/ daemon tools.. then installing the patch.
UT does ask for the CD1 when you apply the 436 patch.
If this doesn't help, insure that you have the correct cd-rom drive selected
