We had exactly the same issue for one developer, and the fun thing is that it started quite suddenly. The DB worked perfectly for months, and then it suddenly stopped working when he upgraded his DB version from 4.2.x or 4.3.x to 4.3.6.
We tried uninstall, delete everything, reinstall; compared class files between installations etc. No luck.
In the end @abk's comment about neo4j-start.ps1 setting the classpath brought us to the right idea. The developer had once installed Neo4j 3.5 using the Windows package manager "chocolatey" (we didn't have any experience with Neo4j Desktop back then). After we noticed this only installs 3.5 (and we wanted to start with 4) we switched to Neo4j Desktop.
Unfortunately, the chocolatey package globally sets NEO4J_HOME environment variable to its own installation (c:\tools\neo4j-community or something). Removing that environment variable and removing leftovers from the chocolatey package fixed the problem, the DB started again.
@dionisios95 if you still have the problem, I suggest you check the NEO4J_HOME variable or delete it. My installation doesn't require it to be set in Windows.
My proposal for Neo4j would be to do more logging inside the startup scripts. We could have found this issue a lot sooner if the startup scripts log their actions. The error message "class not found" is not really helpful if I don't know what the classpath is.
