We are using a Choo Choo mechanism to pull back steel cable for our shooter this year and we are wondering how other teams have prevented their cables from slipping. Any help would be much appreciated. 
You could look into sailing line and tying a bowline at each end.
You could drill a hole through a rotating bolt, pass the cable through and secure with crimps or clamps, either a single block behind the bolt, or loop the bitter end back around for a standard loop crimp.
Another possibility would be to crimp a loop snugly around a pulley or other sheave (e.g. two shaft collars with a gap between them).
I believe you are referring to a way to make sure you don’t slip back down the rope after you climb. if you are using rope (I recommend military 550 chord , also known as Para-chord) then there are a few options available.
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a knot, the types of knots you want are either a prussic knot or a taught-line hitch. These are both knots that can slide along rope but lock in place under a load.
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a repell and belay system, this is used a lot to get people down from high places SLOWLY, but the system provides a way to stop the decent simply by changing the angle of the rope into the belay system.
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commercialy available rock climbing equipment can do something like this.
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a ratchet system. you spool that you attach your rope to cannot be back driven if you put a ratchet system. most store bought winches has a locking ratchet on them