Why can't I rename my folders???

Well when you try to rename a folder what happens??? Some info would help.

I assume you're trying to click in order to rename (rather than pressing the return key).

Perhaps the mouse double-click speed has inadvertently been set to an extremely slow setting, such that the repeated clicks are being interpreted as double-clicks, triple-clicks, and so on, rather than a click-pause-click sequence. You might want to double-check in System Preferences, and also that any Universal Access features haven't accidentally been turned on.

If you're in more of a detective mood, you might try creating a new Cocoa app Xcode project in which you create a custom NSView subclass, then add the following code:

- (void)mouseDown:(NSEvent *)event {
 NSLog(@"[%@ %@] clickCount == %lu; event == %@",
 NSStringFromClass([self class]),
 NSStringFromSelector(_cmd), [event clickCount], event);
}

Then in IB, drag a custom view out onto the default window and set its class to be your custom subclass. Then build, run, and click on the view like you were in the Finder and watch for output in the Console to determine how the clicks are being interpreted.

Sounds like your double-click speed is off. If this is on the MacBook Pro, go to System Preferences -> Trackpad and adjust the slider for double-click speed towards the fast end. (Default is two notches from the right.) On a mouse-using Mac, use System Preferences -> Mouse.