You can trigger the camera through the laptop using the EOS utility. But the flash can only be triggered by the camera because the camera needs to "tell" the flash when the shutter is fully open (that's what "syncing" means). This can be done through the hotshoe signals, a hotshoe-adaptor cable that relays the signals, a simple radio trigger ("shoot now!"), or a more complex ETTL-compatible radio controller. If you can one of the more recent Canon cameras (like the 7D or 5DIII), they have incorporated the "master controller" into the cameras. For cameras like yours, you need either a connection to the hotshoe, or a on-shoe master that can send the appropriate signals to the slaves.
Edit: I'm repeating what Big Mike already said.