There was no nearby store.
There were no nearby stores.
Can anyone tell me whether or not there is any difference between these sentences?
There was no nearby store.
There were no nearby stores.
Can anyone tell me whether or not there is any difference between these sentences?
I think your question is whether there's a difference in using the singular or the plural. Also, I think both of these would read more naturally with "nearby" in front of "store[s]", although what you have written is acceptable.
We can answer the difference between singular and plural--there are some subtle differences--but we need more context to really work out the details, because the differences would be subtle. It depends on what you're trying to say or emphasize; what information is the speaker trying to communicate? What's the speaker's attitude? Is there a particular type of store that s/he is looking for?
For example, I used to live in a commercial district. There was a perfume shop and a cloth shop on the first floor of the building, and a bunch of jewelry stores and bead stores (and shops like that) in the neighborhood, but no grocery store nearby. When complaining about the lack of a grocery store, I might say "There's no store nearby." Obviously there were plenty of stores around, if I wanted to buy beads or perfume! But "store" by itself (at least in my observation of standard US English) most frequently refers to a grocery store or supermarket. "I'm going to the store" without further context means a grocery store, not a hardware store or an automobile dealership.
On the other hand, if I know that I'm looking for a particular type of store, I might use "store" to refer to that--if my housemate and I are fixing our hot water heater and I say "I am going to the store to get some more screws," it's pretty clear I mean a hardware store, not a grocery store.
On the other hand, say I need to return some merchandise to a particular seller, especially a chain store with multiple locations--like Macy's, a department store. I could say "I was going to return that sweater, but there were no stores nearby, so I thought I'd do it later." Again, "stores" doesn't necessarily mean every possible type of merchant; from context it means that particular retailer didn't have any locations near me. I could stand in front of an ice cream shop and say "There are no stores nearby" and no one would be the least bit confused, provided the context made clear that I wanted a different type of store.
So, at a basic level--if you are just describing a place where there are no shops of any kind--either one of your sentences would be fine. But there can absolutely be subtle differences between using "store" and using "stores", and they are strongly dependent on context.