Yes, yes it can.
You are on the right path cables, battery terminals, battery. But before buying something you may not need today or next week check the ignition switch on the top of the column. These have a habit of burning up and causing all sorts of weird stuff.

 

How would I go about checking it?

 

mine used to do that all the time check your gauges fuse. it would blow mine and if it just keeps blowing fuses check the wire to the starter. my engine ground wire melted into the starter wire so it would blow everytime i tryed to start it.

 

Just to clarify, the power comes back on if I move the battery cables around, not just like after I turn the key off or anything. Just throwing that in if something needs clarified....