First thing, check that the power supply is giving the correct voltage on load.
If your unit is in fact dead and you get a replacement of the same revision, then, in theory, you should be able to plug in the old disks (use the same slot assignment) and everything should return to normal. Note I said should, there is no guarantee that it will so you need a full backup of your data.
If you need to backup your data go to the sticky Data Recovery (Windows PCs) and the Data Recovery Using an External SATA/USB Caddy and follow the instructions (I can confirm it works because that is the method I described and JavaLawyer wrote it up for the benefit of everyone. It does require enough free space on the PC hard disk or, if you know how to do it, you can use another external USB hard drive as the destination).