I'm having this problem too with the Steam version of Dark Forces. Well, the Steam version works perfectly fine, but when I try to run it with my local version of Dosbox instead of theirs, I'm stuck with the no-cd error.
I have been able to pinpoint the problem to my version of dosbox: I have installed 0.74, while Steam provides 0.73. After having installed 0.73 myself, I was able to succesfully run DARK.EXE. I juggled a bit with the various dosbox.conf files but it didn't change anything.
All this using Windows 7. I also tried Ubuntu 12.04 with 0.74, where I initially encountered the problem. (I tried bypassing it by duplicating steam/dark and mounting one as a cd-rom but the game then complained about missing HelNum.fnt, a file nowhere to be found. But it's probably because the Steam version doesn't have any of the CD files.)
So there seem to be a regression between 0.73 and 0.74 regarding this game. I haven't tried the nightlies.