Short version: I had this problem myself and figured out a solution--kill wdfmgr.exe in your task manager.
Long version: The game had worked perfectly for me for months until one day it demanded the CD be in the drive. It was in the drive. The CD hasn't left the drive in months. Eject a few times, reboot, the game might launch 1 of 5 attempts.
I had never installed Windows Media Player 10 on my computer but had recently accidentally kicked off the Install Wizard (perhaps fiddling with directx? i don't remember how I did this but i do remember going "no, crap, no! not WMP10! Cancel Cancel Cancel") It appears that WMP10 installs a "Windows User Mode Driver Framework" which I knew nothing about until researching this. It's supposed to help external hardware be recognized... something something... makes sense I guess if you need to synch your iPod or whatever with WMP10... Anyway, it's a hardware driver abstraction layer and I can totally imagine such a thing conflicting with whatever nasty stuff SafeDisk is trying to determine about your system. (It probably appears to SafeDisk that there's emulated drives around or something?)
So, trying to troubleshoot this bastard, I checked my Task Manager, saw wdfmgr.exe running, which I didn't recognize, so I researched it. Found out what it was and killed it with extreme predjudice and CIV4 and Warlords launch perfectly fine 100% of the time with no complaints about needing a CD or DVD. Additionally, this wdfmgr.exe is a service, so you can set it to Manual or Disabled in services.msc.
I hope this helps. Pass this along. This was the "magic bullet" solution for me.