Trying to run tomcat as a limited user on Windows means tomcat doesn't have write permissions to the logs directory. And idea how to solve that (running as admin is not a solution).
Well, to run Tomcat with non-admin priviliges, if the issue is only with writing logs, you may:
However, I don''t think it will completely solve the problem, if Windows have some restrictions like unix regd. port accesses.
For e.g. Unix will not let you start it on port 80/443 (<1024) unless your have superuser privileges. So that is one artea you will need to check on.