Led on when not supposed to be
The behavior you describe is symptomatic of a floating input.

I guess you have directly wired your buttons between input pins and +5V (or GND, that won't change the observed behavior).

The problem is when you don't push the button, the input pin is left floating and can be read as HIGH or LOW based on strange factors.

The solution to this is to use pullup (if you connect the other side of the button to GND) or pulldown (if your button is connected to +5V) resistors.

The following image, off the arduino website, shows such a circuit with a pulldown resistor, i.e. connect the switch to +5V and the resistor to GND:



An even simpler way is to connect the buttons to GND and use pinMode(pin, INPUT_PULLUP); in setup().