I'd be careful with the link provided above; it is quite outdated and for older systems - so, unless your machine originally came with 10.3 or 10.4, the process is simplified. And, there is no longer an "archive & install". So, that brings us to this question:
What OS version did your computer come with? If it came with 10.5 (Leopard) or 10.6 (Snow Leopard), it came with install disks. If you do not have them any longer, you will need to call Apple and give them your serial number - they will send you your machine specific disks for a nominal charge. You cannot reinstall the OS without the disk and, as you can see, you need it now and will need it again if you sell/gift your machine.
If the installation failed with the Combo update, then I'd suggest a reinstall. It is quite straight forward: insert disk, restart while holding down C key, go to Utilities/Disk Utility and choose repair disk and repair permissions, and then erase disk. The installer will then reinstall after that. Make very sure you have a backup of your stuff beforehand that you can copy back when you're done with the reinstall.