FAIL - Failed to deploy application at context path /ROOT. Deploy plugin of jenkins failling to deploy
Just a wild guess but the ROOT context is not: /ROOT but rather / maybe there is something wrong in your config
Its a ContainerExc not fileNotFound; therefore the war file has been located.
URL should be http://localhost:8080
Is userName and Password provided?
Is this userName assigned a role of manager-script?
is the tomcat webapp cleared down once for work and temp folder?
If YES to above all, now run the tomcat without any war fiel present in the webapps folder and open a web broswer to see http://localhost:8080 is accessible. Now whilst this tomcat running, build the jenkins job and deployment should be fine.