I for the past 2 months, my 08 JKU has been throwing fits at times. There's nothing consistent about it, and it doesn't happen with any rhyme or reason. It just happens. It'll start daily for weeks, then all of a sudden nothing. After about 20 minutes of turning the key on and off and on and off it'll finally start. When you try to start it, however, there's no engine lights that come on, nothing clicking to indicate a bad starter, and the fuel pump is buzzing. I'm at a complete loss. Any help is greatly appreciated.

 

Next time it happens, try moving the shift lever farther into Park, or back to Neutral. See if that changes anything.

A few common causes for this are:
Bad Wireless Control Module
Bad Transmission Range Sensor
Bad ground wire connections

 

I just signed on to look for this exact problem on my 08. Let me know if you figure it out and I will do the same.

 

Next time open hood and give the TIPM (fuse box in front of the battery) a few whacks and then try it.

 

Rather than that, if Ronjenx suggestion doesn't work open the hood and the fuse box lid, lift up the white combination fuse holder J13, wait 60 seconds, push it back down until it seats. If this does the job see your dealer and have the Service Action for the wireless control module performed.

 

I was more referring to a bad TIPM as its a very common issue in the 2008s. Ask me how I know

 

I had an old XJ that did this and it was a bad ground in the system. I had some random wire rub against the frame and wear through the covering. Depending on how I was parked, it would either start or not. Finally it died where I had to get it towed to a shop. $46.75 was my bill. $45 in labor to find the bad ground and $1.75 for a new wire.

 

Been having the same problem on my '07 JK. Changed to a new Autozone starter and about six months later started doing it again. Thinking that it might a bad starter, went and bought a Mopar starter and still have the same problem. No codes or lights.

 

Similar problem on my '10, it wouldn't start, no power, nothing but the red security light, turns out it was a loose wire on the battery terminal, where it splits, the wire to the stater was fine but the auxiliary power wire was just slightly loose, this was after I had the battery tested and the starter tweeted

 

Also had no codes