Have you tried to turn the balance wheel? I would try this with it unplugged to see it the wheel will rotate. Tilt the head back and look inside where the bobbin fits and see what condition that area is in. See if it might need to be cleaned out. If it hasn't been run for that long I would imagine it needs to be cleaned and oiled at least.

Does the light come on?

Yes, the light comes on

Thirty years is a long while for a sewingachine to sit unused. It needs to be oiled and perhaps cleaned. You shouldn't try to use it until you can lubricate it (with sewing machine oil). The manual will instruct you on where to oil. Most Simger manuals can be found online.

It's a good model, well worth spending some time and effort on it. It looks like it's in very good condition, a bit dusty thats' all.

Yes, it can probably be fixed. Usually what happens is that the oil solidifies and gums up the things that should turn.

1. Take it out of the cabinet
2. Find the maintenance manual
3. Get a spray can of WD-40
4. Set up a place where you won't have to move things for a while. Time will be your friend.

Take lots of pictures as you do this, so you can put things back together.

1. Remove the needle, bobbin and cover over the bobbin area.

2. Remove the bottom plate or cover and the cover at the needle end. That should reveal all kinds of rods and things.

3. Place the machine on something absorbent and spray all the places where rods go into other rods or other pieces with the WD-40.

4. Let it sit and soak for a few hours.

5. Spray them again, and by hand, try turning the wheel slowly.

6. Wipe off any gunk that comes out, let it sit some more

7. Repeat until things turn easily

1. Then, do the regular lubricating with the sewing machine oil and grease like the manual says and put it back together.