Firstly, Apache is a service run on top of the operating system. As such, it has no notion of network drives, be they NFS (for *NIX) or SMB (for Windows) or even AFP for (OS X) -- unless I'm sadly mistaken.
Make certain that the operating system running the apache server has the network drive mounted *before* you start the apache service. If you can't browse the files on the remote drive, apache can't serve them. In *NIX, this might mean auto-mounting an NFS mount. In Windows, it will most likely mean mapping a network drive at boot or login or something like that.
If the files are available, check their permissions (filesystem). As well, when apache blows up, it should log what problems it encounters somewhere. Check those out -- they'll be helpful.
All that said, you might also be aware that serving files from remote filesystems can cause problems, not least among them lag in times of heavy network use.