Go down to the starter with a volt meter. Check for about 12V on the small wire (probably PPL color) while trying to crank. If you have that, then check voltage at the large terminal on the starter, where the battery cable connects. Use the starter case for the other meter lead during these tests, not just some handy chassis metal.
Same idea as billr suggests, just a different twist.
Run a temporary wire from that small starter wire (probably PPL color) up close to the battery + positive terminal. Now touch it to the bat +. If the starter works you have a problem getting voltage to the starter solenoid. If nothing happens you have a starter problem. Simple. In fact I have that wire permanently installed on my cars so that if I ever have a no start problem I can instantly diagnose it without getting dirty.
As billr states "Now we need the schematic for the ignition switch on down to the starter..."
Your problem could be the ign switch, clutch switch, brake switch, neutral safety switch, starter relay (you stated you switched it tho) and something that is probably not allowing ign voltage, fuel pump voltage and /or???
I don't think I need to ask you this, but do you have dash lights, etc. Just wondering if the fusable link blew? Just covering all bases.
Apply 12 volts to the feed at the relay and see if it cranks. This will narrow down what part of the circuit is bad.
I'm getting posts mixed up. I thought you checked the switch but after revies I see you didn't. Check the ignition switch.
If this was an older GM car, I would be saying that the security feature needs to relearn the "key code". For 2010, I don't know what the situation might be for Passlock, Passkey, etc. But I thought I should mention the possibility as a cause of your problem.