Ok, so your first problem is this:
Play server process ID is 5120
This application is already running (Or delete C:\dev\eslfish\RUNNING_PID file).
Either Play is already running, or something has gone wrong. Check the Task manager to see if there are any java processes that might be from Play, and kill them. If there are none, then delete C:\dev\eslfish\RUNNING_PID.
The second thing is, the best way to run Play in production is to produce an artifact by running "play clean compile dist". This doesn't have to be run on the production machine, it will produce a zip file in the dist directory of your project. You can then copy this zip file to your production server, unzip it, and it contains the lib folder with all the Jars that Christian talked about.
Let us know if you have any problems with that.
Cheers,
James