First house just north of the B & O railroad tracks and the Blackland Elevator, along Hwy 27 (now Lincoln Memorial Parkway). There also used to be another house located to the west of this house, behind the elevator, but it burned sometime in the 1980s or 1990s (?) If anyone knows when that other house burned, please add a comment here!

My grandparents told me it was an old store.

Hi WeRemember:
The old grocery store that you were told about wasn't the house that burned down (which was just a small house located out in the field west of the house that is visible in this photo) but instead the store was located out near the road (Hwy 27 or Lincoln Memorial Parkway) . If you look at this photo:
https://vintageaerial.com/photos/illi...
See that faint white sort of square spot to the immediate left of the tree (the tree in about the center of the picture)? That is the "footprint" of the old store which was run by some people named DIAL.
I don't know anything about them other than they ran a store there for some time (perhaps in the 40s / 50s??) The bottom floor was the store, and their living quarters were the upper story of the house. The tree there is a Osage Orange (also called a Hedge Apple) and me and my brother would go down there sometimes, and play on that concrete pad (that was all that was left) and pretend it was our house! Ha! I think the Osage orange tree still stands today.

Edit: Another view from 1967 looking to the west shows that other old house that no longer stands - it was farther west. https://vintageaerial.com/photos/illi...

An elderly woman lived in the small blue house by the elevator. She ran the store during the time my great grandparents lived at Blackland. She used to walk down to their house on Sundays to visit. She had a dachshund that she carried with her. All according to my gma.

Hi WeRemember,
My Mom knew the lady who lived in that house (currently painted blue) back in the mid-1960s and I will ask her if she remembers her name (she is 91). I'm not positive if it is the same woman your great-grandparents knew, but it may have been.
In about 1967 or 1968 a young couple named Tim and Marsha McLemore moved into that house. No idea how long they stayed there, as we moved to AZ in 1969.