You are getting all those unmet dependency errors because you are trying to install software on a version of Ubuntu that has reached end of life and therefore it's no longer supported. The sensible thing to do is to backup your data and do a fresh install of Ubuntu 14.04, which is also a Long Term Support release like Ubuntu 10.04.
Alternatively you could do a fresh install of Ubuntu 15.10. Ubuntu 15.10, which will be released in a few days on October 22, has almost the same version of rabbitmq-server that you are trying to install in its official repositories, so you certainly won't get any errors if you install rabbitmq-server 3.5.4-1 from the Ubuntu Software Center in Ubuntu 15.10.
Instead of doing a fresh install, you could also try to upgrade Ubuntu 10.04 to Ubuntu 14.04 by following the instructions in Can I skip over releases when upgrading?, however this is liable to result in a misconfigured system.