Thanks for this advice #CarTalkNation, I am looking into other mechanics now!
I can think of a few reasons this could happen, but that’s not the issue. The issue is that the service department at the dealership is incompetent.
I vote with the idea that you have the car towed to another mechanic.
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That’s a pretty unusual diagnosis. … hmmm … I’m not familiar w/the s2000, but I’d guess is doesn’t use any valve sensors, but does use a “camshaft sensor”. That sensor would detect the rate the camshaft is turning around in a circle and its phase in relationship the other major engine shaft, the crankshaft. That info is necessary for the ignition system to fire on the compression stroke and not the exhaust stroke. The camshaft is what pushes down on the valves to open and close them, allowing air and gasoline in and exhaust out, so maybe that is what they mean, there’s something wrong with the camshaft. The sensor wouldn’t touch the camshaft, so wouldn’t affect engine turning; I suppose a bent valve stem could jam in the valve guide area & lock-up the camshaft when the engine gets hot, so that might be one way to interpret this diagnosis. I’ve never heard of that happening though. If that’s the case, the problem might be limited to the cylinder head rather than the entire engine.
A couple of questions you might ask
- Is there a mechanical interference preventing the camshaft from rotating freely? If so, what?
- Is there a mechanical interference preventing the crankshaft from rotating freely? If so, what?
- Is the engine compression affected?
I hope you don’t have to pay for the starter, battery and cables. Like other already pointed out, it could be a ton of different causes. A few days ago I had a similar issues with an Acura CL, has a Honda engine and parts in it. I cleaned a filthy idle air control valve. One of the inlets has a tiny mesh filter/screen, which was dirty and kept air from flowing when needed. Caused failed starts and rough idling and stuttering on sudden acceleration. Took me less than an hour to remove this thing and clean it. Starts perfectly and he engine runs smooth now. (besides some other issues, but that’s a separate story).
Your reiteration of the details seems very jumbled drawing more insults toward the repair industry.
From your description of the symptoms and some of the word used in the “diagnoses” I suspect that the variable valve timing camshaft actuator is sticking resulting in an engine stall and difficult restart. If the cause of the malfunctioning variable valve timing system is a sludged engine this would explain why they recommend to replace the engine.
Again, many thanks to all for sharing your insights with me.I have set up a meeting today @ the dealership (tow-truck on call, too) #BeSafeBeWell
Just to clarify my comments, should it be needed, I was insulting the specific mechanics working on OP’s car, who are, if OP is remembering what they say correctly, morons.
More generalized comments on the relative intelligence of the rest of the repair industry should not be inferred. 
and BTW, I’ll point out again since it was awhile ago, that they apparently decided the running but sputtering engine would be fixed by replacing the starter…
The person who started this says they are going to move the vehicle to another shop . That is a good move but it would be interesting to hear all sides of this saga. At least with this S2000 a new engine is not a waste of money and hopefully the next service garage can explain the problems and solutions better.