When you buy a spray can, and it doesn’t work, is there a way to fix it, without having to go back to the store and exchange it?

Very, very rare to have a manufacturing defect that prevents the can from working.
The most likely cause is that the nozzle is clogged. Now, how would the nozzle get clogged?
Assuming this is a can of spray paint, almost certainly someone “checked” it in the store, to “see” what the color is. Couple of quick bursts onto the floor or the rack. In most Home Depot stores, the concrete floor of the spray paint aisle is extensively decorated with these “just want to see” trials.
Actually, if you stand at the end of the aisle and watch people “test” the cans, nearly always they will then put the can back on the shelf, and take another one that “has not been used”, so they get all the paint they are entitled to — not having to buy a can that is “partly used”, even though it was them who actually did all the using.
The “tested” can sits on the shelf, and the spray residue dries out in the nozzle. Hence, it doesn’t work for the customer who actually buys the can, considering into be completly new and unused.
A significant fraction of the store’s inventory is actually destroyed in this way, by thoughtless and irresponsible customers. Often, they are not customers at all, but people who are “just looking”.
The same problem occurs with other kinds of spray cans, which become clogged with dried hair spray or deodorant or bug killer or whatever else is being offered.
You really have no protection. Just take the can back, and point out that it has evidently been “tried”, i.e., (mis-)used, and ask for a replacement. The weary and exasperated clerks will replace it, and the store will throw out your can, suffering yet another loss caused by people who don’t know how to behave.

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