Hi Sella,
As suggested by Antoine, try modifying the Tomcat properties.
In addition, there is no direct relation between Adaptive Processing server and Apache Tomcat. If you feel tomcat is not running, you can directly check by http://127.0.0.1:8080/ URL in Server's browser.
Also you can check in Windows Services (using services.msc command in RUN) if Apache Tomcat is running or not.
Please take proper backup and try to repair your BO setup. If it does not fix your problem, please raise case with SAP support as their hands-on dignostic can fix your problem.