Can't be connected by car = a regular individual can't drive a regular vehicle between the two countries, including via another country.
I'm not interested in the case where driving is made impossible because of some military conflicts, e.g with North Korea.
I'm aware of (Panama, Colombia). Is there any other such pair of countries?
There are no roads connecting Suriname to any of its neighbors (France, Guyana, or Brazil), though there are ferry connections over the rivers to Guyana and France.
(Wikivoyage says that there's a road between Suriname and Guyana, but it's wrong: satellite imagery clearly shows a hole in the road, and travelers' reports clearly state that a transfer to and from the ferry is required.
The Italian Republic and the Vatican City State
Wikipedia states
The Vatican City State, also known simply as the Vatican, became independent from Italy with the Lateran Treaty (1929), and it is a distinct territory under "full ownership, exclusive dominion, and sovereign authority and jurisdiction" of the Holy See, itself a sovereign entity of international law.
The page Travel to Vatican City states
Driving: In Vatican City, they drive on the right side of the road, but it is highly unlikely that you will ever drive inside the Vatican. The only way the public can drive in the Vatican is if you’re there on official business and enter a via parking lot near St. Ann’s.
So it qualifies under OP's conditions
a regular individual can't drive a regular vehicle between the two countries
there is no ongoing military conflict preventing it
Canada and Denmark have recently announced that they will divide Hans Island between them. Hans Island is a small uninhabited island in the middle of the Nares Strait between Greenland and Ellesmere Island; before this treaty, both countries had claimed ownership of the island.
This treaty, once ratified, will create a land border between the two countries that cannot be driven across; the island is uninhabited and there are no bridges leading to it.
Various Antarctic territorial claims provide "land borders" that cannot be crossed due to the lack of roads, including:
None of these countries share a land border anywhere else in the world, of course. EDIT: As was pointed out by Nate Eldridge in the comments, it is possible to drive from Norway to Gibraltar, which is also a British Overseas Territory; so the last of these does not qualify.
For the purposes of this question, it is probably best to draw a discreet veil over the conflicts between the claims of Chile, Argentina, and the UK, as they make the concept of a "border" ill-defined. The Chile-Argentina border on the South American continent is relatively easy to cross anyhow.
Singapore and Malaysia are connected by a causeway and a bridge, with the Causeway in regular times being the world's busiest border crossing by some measures.
However, due to COVID-19, for much of 2020-2022 both were completely closed to private passenger vehicles: the only way to cross was by designated bus services. Both links reopened on April 1, 2022.
If you're willing to stretch the definition of "connected by land": the UK and France are connected by land, namely the Channel Tunnel.
You can't drive through it as it consists of two train tunnels plus a pedestrian service tunnel - though you can take your car on a train.
