If the application is executing directly as a bootable compiled executable, then I dont see how you will extract any part of it that would be useful.
If it is a Windows thingy, then CTRL+Alt+Del might bring up the Task Manager which should allow ending program execution of the start up program (but this might be disabled as part of customization).
Yea lots going on here. It could be custom software/OS bundle and no matter what you do, you wont be able to just extract the program. Your best bet might be to do a bit-for-bit disk clone with something like acronis. Then test the new disk and save it for later, or find similar hardware if you need multiple installs. Potentially you could do a physical to virtual migration, and take the software virtual inside vmware as well.
If its a Windows app (you'd know by the Windows boot screen), then yes, CTRL+ALT+DEL should allow you to bring up the taskmanager, and kill the app. Could be that they've disabled explorer.exe so you wouldnt see anything but a blue screen. But with taskmanager you could use it to start a 'new task' from the applications tab and start explorer.exe
Its pretty difficult to disable the CTRL+ALT+DEL I believe without hooking the kernel.
You can swap explorer.exe (Windows Shell/GUI) for another application. This is done in the registry somewhere. Thats how shell mods like litestep.exe worked (you can actually put a new GUI on windows). So I'm sure there are some kiosk programs that do this. Again CTRL+ALT+DEL should get around this. Once into explorer.exe with this or safemode you should be able to disable the app and restore explorer so the computer boots normally. Then see if you can extract the app.
If its Windows you could try Safemode with F8 during boot.