I don't have an answer (yet) for you, but I have a 09 JK and about 1 - 2 months ago it began doing the same thing, turn the key ..... nothing.
I actually today posted a help request from the experts in the forum and have received great replies (thanks everyone).
I feel I am heading in the right direction and have learned alot in just one day.
The biggest thing I have learned is this is a well known problem (that I have just learned about) and there is a TSB "08-007-08 Rev. A" that deals with this specific problem "No crank, no start".
I read about some guys having success by simply disconnecting their batteries for 30 minutes, I have done that a few hours ago.
I also looked inside my fuse box and ensured the relays and fuses were secure, some appeared to be sligtly loose.
I am still dealing with this myself and am taking my JK to the dealership again the next time it does it, but this time I know about the mentioned TSB.
See my post from today, titled something like "09 JK Starting problems", there are some great leads as what to do to fix this.
Best of luck. Please let me know what the problem was if you find out, thanks!