Alan,
You are right in needing +ve on pin 8, and 0v on pin 4. Also you do need a ground to tthe computer to complete the circuit as you suggested.
The NTE 943 is a comparator, and can run from 5v to 30v see data sheet http://www.nteinc.com/specs/900to999/NTE943.html
Your circuit is designed to give pulses when the light level changes; it is not intended to show two states, light and dark.
Under steady light conditions pin 2 is at half voltage so adjust the potentiometer to make pin 3 just below half voltage. Pin 1 will be low because pin 2 ( inverting input) is higher than 3, but pin 7 follows pin 5 ( non inverting input to second stage), so pin 7 is low and LED is on.
( the reason you 'are always high' is probably because you have set the potentiometer to make pin 3 higher than half voltage)
Shine a light on the cell and it reduces resistance so pin 2 gets pulled low, 3 goes high, 7 goes high and the LED is off, but only while the 22uf capacitor is charging. So you only get the LED off for a while.
If you want it to stay showing the light level, instead of a pulse, just remove the 10k resistor and the 22uf capacitor.
You didn't say which light cell you use but if you can get an ORP12, it's been around for 30 years and still the best device around.
(Also because this circuit is designed to only give high or low output, not progressive,  don't bother to try feeding it into an analogue input.)
Baz