If it's cranking fine, it's not the battery. As you suspect, almost certainly lack of fuel or spark. Not the plugs either.
First check all fuses underhood, especially those for fuel pump and injectors.
The next easiest thing to check for is fuel. You'll have to pop the left side plastic rail cover to check for this...At the front end of the left rail, you'll see a plastic cap covering a shrader valve. (same type valve as on tires). Remove the plastic cap, but don't depress the valve just yet.
Get a rag or bunch of paper towels and a tiny screwdriver (or similar to depress the valve core) ready.
Now attempt to start the engine as normal...Let it crank for a while. As soon as you stop cranking, get out and holding the rags in front of/under the rail, briefly depress the valve core.
-If you get a strong stream of fuel shoot out, you're getting fuel to the injectors, and it's something electrical.
-If you get a drip, dribble, or nothing out of the rail, you aren't getting fuel.
If no fuel, and pump fuse is good, you may want to read this thread about the fuel pump relay...This seems to be not that uncommon of a problem...
2005 C6 cranks but won't start - no fuel - Corvette Forum
If you are getting fuel pressure and all fuses are good, I'll have to think some more as to where to start looking next, but I'm suspecting no fuel if you're not seeing any codes.I believe anti-theft intervention should prevent cranking, and/or throw a related code.