The possible approaches are:
- install a larger hard disk
- perform a 1:1 copy of the data from the old disk - e.g. by mirroring the old disk using Windows Disk Management or employing a 3rd party Live CD
- remove the old disk
- expand the partitions / filesystems using 3rd party utilities (see below)
or
- install a larger hard disk
- copy the partitions expanding them simultaneously using some kind of 3rd party software (see below)
- do not forget to copy the boot block and make sure your newly copied partitions carry the same attributes (especially the "Active" flag) and types as the old ones
- remove the old disk
or
- do a full backup (including system state) of your server system
- install a new hard disk, remove the old one
- create a new partitioning scheme suiting your current and future needs
- restore from backup (this would involve installing a fresh instance of Windows Server 2003 first when you have used
ntbackup
to create the backup)
Windows Server 2003 does support the expansion of volumes but it does so for non-system volumes (i.e. not the one where your "WINDOWS" directory is) only. If you need to expand the system volume, you would need to resort to 3rd-party tools.
There is a number of commercial software packages for re-partitioning and partition / filesystem resize operations. There also are open-source Linux based LiveCD solutions like the GParted project with a pretty wide range in hardware (controller drivers) support and a broad feature set (resizing / moving partitions, resizing FAT/NTFS/extX filesystems).
If the system partition is the only (and thus the last) partition on your disk, you could use a Windows Server 2008 / Vista / Windows 7 DVD to start the recovery mode and use the command line to invoke "diskpart" to extend the volume as described in KB 325590, thus removing the need for involving non-Microsoft software in the process.
If the volume in question is on a FakeRAID device, you are very likely to encounter problems with any solution, so the recommended approach there would be creating a full backup and replaying it on a new installation.
In general, you should take the route you feel most comfortable and confident with. If you have never used partition editing utilities, you might prefer the backup/restore approach, although it would mean a longer downtime period and more manual work for the admin than the other two. Under no circumstances should you use partition editing utilities which have little prevalence in the market and thus have not been widely tested by a large number of users in most of the possible use cases.