I installed the HP download (and update) a week or so ago and the install files are still on my machine. I installed it after reinstalling Vista, so I didn't have a previous version, though.
I found TrayApp.msi in the C:\Users\Ed\AppData\Local\Temp\7zS4941\setup\trayapp folder.
Given that I didn't have your problem, even if you find it there it may not work if there's a problem with your msi registry entries. In that case, I'd suggest running the 'Windows Installer Cleanup' utility, as described in the link in osholt's last message.
If that doesn't do it, use Revo Uninstaller Download Revo Uninstaller Freeware - Free and Full Download
, selecting the Deep Scan method after normal uninstall to remove leftover files and keys and completely reinstall the app.
Hope this helps.