Do you see no difference at all with "Snap to Grid" disabled? The behaviour of the grid depends on the current zoom setting.
Perhaps your GarageBand preferences file is unreadable. I'd first check, you can disable the grid, when launching GarageBand from a differentt user account, for example the Guest account. If that works and GarageBand is behaving well, use HangTime's oddball probs fix and trash the preferences.
Move com.apple.garageband.plist from the Preferences folder in your user library to the Desktop - see the FAQ:
http://www.bulletsandbones.com/GB/GBFAQ.html#oddballprobs
(Let the page FULLY load. The link to your answer is at the top of your screen)
This usually solves problems with unresponsive user interface elements - the preferences file stores the layout and settings of the interface elements, and if that file is corrupted, some controls may cease to work.
Your user library is hidden in Mavericks. To make it visible in your Home folder (the folder with the little house icon) open a Finder window showing the Home folder, then press the key combination ⌘J to show the View Options. In the View Options panel enable "Library".
Quit GarageBand, if it is running.
Now open the "Library" folder and go to "Preferences".
- Drag "com.apple.garageband.plist" from "Preferences" to the Desktop
- Also go to "Containers" and drag "com.apple.garageband10" to the Desktop.
- Also go to "Caches" and drag "com.apple.garageband" to the Desktop.
Reboot the system.
And try again.
Léonie