Installing PostgreSQL 10 On Windows 7 (yes the clock is ticking...). I first tried the latest version 11 which completely failed to install... not a good sign for Windows users. Anyway.
Quick answer: Change the account in the Windows Services panel from Network to Local.
Details of my case
During installation I created/selected a data folder in the user profile folder, because obviously the folder suggested by default, within the program folder, wouldn't work, and if it worked it would be a very idea to put data here (I don't know whether it's usual to do that on Unix/Linux, but for Windows it's it's not allowed for a long time).
At the end (when populating the data cluster) I received an error:
Failed to load SQL Modules into database Cluster
but the installation was able to complete. I found two pages about previous error, here and here, but they didn't seem relevant to my case, so I just started pgAdmin and, on the left "browser", saw the server wasn't active.
I tried to start it from here (had to type the main password), but it went inactive immediately again. So I tried to use the Windows services panel to start "postgresql-x64-10", no joy. I copied the command from this panel and pasted it into a Windows console (cmd.exe) where I finally received this
error 1063.
Searching I found this related question, and was convinced the problem was about permissions.
Solution working for my case
In the services panel I changed the account used to start the service from Network Service to Local System as suggested in a comment by @AlexanderRios.