I'm guessing you have the updater pointing to Everquest2.exe in both of the top two boxes in the options menu. Set the second one to EQ2.exe (if it exists) or Launcher.exe to have the launcher run and then you can log in there. If you launch Everquest2.exe directly you get a login screen since you skipped the patcher.
As for the server being busy, maybe you were trying to log in during a patch or downtime, that's SOE's end.
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