I'm currently in the process of restoring an old vintage refrigerator and turning it into a kegerator, so I'll try to speak from experience here. The first thing is checking if it runs. It could be just a matter of cracked wires or a bad starter relay. If the problem is electrical then I'd say it's not a deal-breaker because you'd probably replace that stuff anyway during the restoration. However if you can get power to it and the compressor is spinning but no coldness, that'd be a deal-breaker since it probably lost all its refrigerant (Probably Freon) and that would be difficult to deal with to say the least.
If from here you decide to go for it just be aware you're getting yourself into a big project. Also with this comes a decent budget. Originally I was thinking my restoration would be a few hundred $$, but I've gone well past that already between getting new tools, sandblasting, sanding, rust-proofing, paint, replacement parts (door seals, insulation, bolts/screws, thermostat), etc. It seems I'm always running to the hardware store and spending $40-$75 each time.
Not to discourage you, cause the end product is really cool, and you made it yourself! That's the reason we do these things anyway. I just want to help give you a realistic understanding of the job.
Also it's a common misconception that these older fridges/freezers are energy hogs, they actually are comparably efficient to today's appliances. It's when they first came out with the auto-defrost cycle, back in the 70's I believe, what was so inefficient. But if you're turning it into a keezer you'd probably replace the entire thermostat anyway and get rid of that function if it even had it. Add a small dehumidifier in there so you never have to worry about moisture, replace the old insulation with new stuff and it'd work just fine without costing a ton to run it.
Let us know if you decide to go for it!