Do you launch Quark when you boot your computer or at another point after? Do you have any other programs that are activated to launch on start up? Is it a version of Quark that requires Classic to run? All of these may be factors in causing Quark to boot slowly, if the problem does not reside with Quark.
For example, if both QuarkXpress and a font manager (such as Extensis FontSuitcase) are both checked in your start-up panel to launch at the same time when your computer boots up, it could take a while for the system to return control to you. If your version of Quark requires Classic to be active when you launch it, your system will begin running Classic under the OS X shell and finish the launch of Quark when Classic is finished.
In this example, the system is launching two applications and running a check on the font database at the same time. And if your version of Quark is 5.0 or earlier, Classic is also being launched at startup (or whenever Classic is inactive when you launch Quark.
If it's just Quark all on its own, I'm afraid I don't have an immediate answer. Could be Quark may be going through a long list of checks (for XTensions, for example) or is looking for something that isn't always available at launch time, but is not required to run the program.
Brady