Thanks for your complete reply @red2.kerr
We have solved the problem this morning. In our case the solution was as easy as adding the HOME user environment variable.
In addition to this thread, I found two more threads in this community related to this problem when updating R to version 4 and/or RTools 4.0: 63265, 62958. The solution to the problem is related to the environment variables.
Nevertheless, I do not think the problem is directly related to R 4.0.1, nor 1.3.959 or even RTools 4.0. It is more a problem of Windows that cannot find some dll when trying to install some R package (stats, for instance). Discussion of similar errors can be found at:
Hope it helps.