AcroTray should be in your Acrobat or Distiller folder (on my PC is in C:\Program Files\Adobe\Acrobat 9.0\Acrobat). Include AcroTray in the startup folder. If it is missing, you may be able to get it back by running a repair on Acrobat. The cleaner and reinstall should only be done as a last resort. If you do go the cleaner route, be sure to open Acrobat and deactivate it first so that you do not lose one of your activations under the license.
Since you tried the repair and update, you will most likely need to reinstall as suggested. AA9 Pro can be downloaded from http://helpx.adobe.com/acrobat/kb/acrobat-downloads.html, but as TSN said, you still need the SN, not your Adobe ID. As long as you registered your Acrobat, you can open a new tab in your browser window and go to Adobe.com. In the upper right you should see your name (based on your Adobe ID) and select the small arrow and look at your My Products. The SN should be there. If Acrobat is still installed, there are techniques that may recover the SN from your machine.