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I would surmise - though I cannot see the camera nor did I see it get dropped, nor did I see how it landed when it was dropped - that the zoom lever is misaligned with the case, owing to bending of parts caused by the landing.
What 'cover' is it that when off allows the zoom lever to work?
It must be: it was subjected to mechanical shock (depending upon which side hit first when it was dropped.) That is likely to cause slight bending, by perhaps 1 mm, which is enough to limit the travel of controls when the cover is placed back on.
I don't see any other alternative under the circumstances.
To get the zoom lever back into working order, it may have to be bent, towards the back of the camera, very slightly.
Such bending must be done in such a manner that excessive force is not applied! this will be hard to do by hand, for any person attempting it.
An alternative: to use a carving tool or dremel grinder, to make a slight removal of the front case where it now impinges against the slightly bent-forward zoom lever or zoom lever assembly/dial/whatever. That may permit the front case to be put back on, but the zoom lever to also work properly, without the hazardous and difficult process of bending the zoom lever assembly back ... which could easily result in bending it too far, or the bending or breakage of other parts of the camera. So I suspect this last alternative would be the most likely to have a favorable result.
To tell which part of the front case need a slight grinding away or removal, there are variou methods. Let me know if you are interested in being instructed further on this.