I recently had an issue where Launchy stopped appearing when I used the Hotkey to display it. Killing Launchy from Task Manager and restarting still didn't make the Hotkey work.
The last piece of software that I had installed was the Google Desktop, so I started my investigations there. Google Desktop has a Launchy-like feature whereby double-tapping the Ctrl key makes a search box interface appear.
By typing into the box, a drop-down appears giving you the ability to search the web or your desktop, and also displays likely matches. Because it indexes the Start Menu you basically get Launchy-like functionality.
I exited the Google Desktop and restarted Launchy. The Launchy Hotkey was now working again. If I then ran Google Desktop again, so that both applications were running, the Hotkey's for both were then working.
Google Desktop runs when you start you computer because of the Registry key stored under HKLM\Software\Microsoft\Windows\CurrentVersion\Run. Launchy differs in that it adds a shortcut in the Start Menu Startup Folder.
If you really want to run both applications at the same time, the best way to do this would be to put Launchy into the Registry, and Google Desktop into the Startup Folder. Alternatively, there are a number of programs such as the Startup Organizer that promise to let you set the startup sequence of all your processes.