This is why I would create a c:\wininst folder and dump the CD worth of files. When I needed to do an OS reinstall, I'd boot to DOS mode, cd \wininst, and do the install from hard drive to hard drive. Much MUCH faster and much MUCH less painful.
Having the CD dump on the hard drive was a must in the Windows 9x days because every time you would want to add a device, a network protocol or whatever it would ask you to insert the CD. I rarely ever installed from the actual CD directly but always copied it to the hard drive first. Obviously there there were exceptions because some computers just had too little of HDD space so you had to save it for your user files and the apps to be installed (this also is the case with 120 GB MacBooks nowadays - I can't afford a Windows VM on it).