Mom2boys -
First, thanks for the laugh calling a machine from the 1980s vintage! I regularly use the Elna I received when I started college in 1978! And my two back ups are an Elna from 1958 and a Singer from before that!
Ok, more seriously - do try the oil and working on getting the dust out. If there is a brush with it use that to work the dust out of various areas.
Another thing to look at is on that flywheel see if there is a screw (a big one) on the end sort of in the middle. Often on the Singer machines this would be loosened and tightened in opposite directions to determine the machine running or winding a bobbin. Also when you try it you may have to gently start the flywheel turning with your hand. Check the manual to see which direction it is supposed to turn! Over the years I have found that this isn't standard even within the same manufacturer. And if you're trying to turn it the wrong way it simply won't move.
You said the light is coming on but are you getting any noise from the motor? You know sort of like it is trying to run but nothing is moving? Look at the settings too - around that time, especially on the more portable machines, there were lock settings that kept everything from moving when the machine was "packed". The idea was that this would prevent the mechanisms from being damaged. The little Elna I use all the time has this and even though I use the machine all the time I sometimes forget to unlock it. NOTHING happens then. On my Elna there is a knob on the end, not sure what it might look like on that particular model Singer.
If all else fails then a trip to a sewing machine store with it, sounds like it is small enough to be reasonably portable should do it! And hopefully without too much expense!
Deb