Why don't the keyboard shortcuts work?

Reassign those Key Commands in Logic, or look in your *System Preferences* to see if the control key is assigned to something for OS X (Spaces, Exposé, Keyboard & Mouse) effectively 'stealing' the Keycombi from Logic.

To view and edit Key Commands in Logic, press ⌥-K.

The 'flashing' tells you the same as the 'beep' when you hit an invalid keycombination. It could also be that you hit a command that cannot be executed, because you have nothing selected, or because whatever you do have selected can't be edited by that particular command.