There are 2 common problems with ComputerCraft in Tekkit, but both can be easily fixed server-side:
1. Fixing ComputerCraft (General)
To get ComputerCraft running, the folder ComputerCraft in the /mods/ folder of the Tekkit server has to be renamed to ComputerCraft.
2. Fixing Disk Drives
Fixing this requires downloading the latest version of ComputerCraft ported to Bukkit.
You can find it at http://www.mcportcentral.co.za/index.php?topic=1360.0 scroll down on that page, until you find ComputerCraft 1.3 r5 and download it.
Do not download a later version of ComputerCraft, this would require all clients to have it installed too.
Extract the zip and put the folder ComputerCraft you found inside into the /mods/ folder, which means replacing the old one with it. If you didn't follow step 1 of this tutorial, you should delete the ComputerCraft folder now.