Although train was not a viable way to get around Ethiopia at the time of writing, it may well be by the time you read this.
Major train infrastructure projects are currently underway, with the following sections completed or under construction at the time of writing:
Dire Dawa–Djibouti Completed but of little use to domestic travellers.
Addis Ababa–Dire Dawa Largely completed and due to open shortly.
Addis Ababa–Mekele Under construction, but probably a few years off completion.