Apple II in Lost - Season 2 (2005)
The Apple is in the Swan research laboratory and it is required that a sequence of numbers be entered on it every 108 minutes.
The machine is of the right era for the Dharma Initiative, but the Apple II keyboard does not have an EXECUTE key that is so prominent here. They also appear to switch on the machine using the monitor's power button.
Nice shots of the Apple with the lid off, here!