Hi Adam
I have no idea what Jenkins is (I had a look as I've not heard of it) but I'm guessing that it's this:
https://wiki.jenkins-ci.org/display/JENKINS/Starting+and+Accessing+Jenkins
On that page it gives one of the startup command line options as --httpPort so I'd suggest you try adding --httpPort=80 to the startup command line and see what happens.
Thanks! I found where I think the Jenkins command line is:
/etc/init.d/jenkins
but adding httpPort and restarting just kills Jenkins. I realise you're not familiar with Jenkins, so this is just an update really. I need to track down the logs too.