Bicycle Tutor

Hey there,
I have an old mountain bike with Shimano Altus c10 gear system. It's been unused for years, a bit old and rusty. The point is that I found that its rear shifter (the one on the right hand) does nothing, it's loose and it seems that the wire doesn't move, no mather what I try. Is there any solution for that? May the wire be broken? Is there any way to open the shifter and fix it?
Thanks a million in advance,
Germán.

Undo the cable at the rear derailleur.
Now get hold of the cable "outer" at the shifter end and pull gently.
This should expose the inner cable where it goes into the shifter.
Once there is some exposed cable try operating the shifter.
If the "outer" doesn't move then the cable is seized. If the shifter is seized then try some release oil. You may be able to part strip the shifter for better access. ( I think the top cover may come off.)