Yup it's a push-pull zoom alright.
No zoom is usually(as agx said) somethings loose or broken.
Frequently a roller in the zoom cam. If you're lucky it's under the rubber grip.
The grip slides off but needs some delicate lifting/prodding, just start at one edge and work
around the lens.
If nothing seems awry, you gotta go a bit deeper. MARK THE STARTING POINT SO YOU ARE SURE IT"S IN THE SAME PLACE AS WHEN YOU BEGAN.
It's amazing how many starting points there can be in there if you get it bolloxed up.