I had this same problem on my 2004 EFI a couple of weeks ago. Here is what I tried and figured out.
My battery had been on a battery tender for a couple of months while i was away on work. I got back and I got the same thing. Pod lit up, key turned, click, nothign from the engine.
1. Put a battery charger on the battery. It read fully charged immediately so either the battery really is charged or it isn't going to take a charge.
2. Checked the battery connections. They looked clean but I took them off and cleaned them with a wire brush and some coke anyway. Put them back on. Stiill just a click.
3. Tried jumping it with my wife's ATV and my Dodge. Neither got me more than a click. So at this point I am almost positive the battery isn't the problem. If it was I should have been able to jump it.
4. Try tapping the starter with a hammer while turning the key. If the starter is beginning to go bad this should break it loose and get it started spinning. Didn't work for me. This doesn't confirm the starter is bad. If it had started turning then I would have known. Instead this test didn't help at all.
5. Pulled the air box so I could get directly to the starter. I put the jumper cab;es from the battery to the starter, bypassing the solenoid. I can hear the starter drawing power but it still doesn't turn.
6. So at htis point I know my battery and my solenoid isn't the problem. Either the starter is bad or the whole engine is frozen. Doing some reading I found starters to be a not uncommon problem. So I pulled the starter out (thankfully a ver easy job on our model compared to some others.) I hokked the jumper cables directly to the starter and it didn't turn, but if I hit it with a hammer while hooked up it would turn about 1/8 of a revolution. So there we go, my starter is frozen.
I opened up the starter to look at it. it looked like a toxic waste site with corrosion and mud. so I ordered a new one on ebay from DBELECTRICAL. Mirrors, Starters Tractor items in DB Electrical-Starters-Alternators store on eBay!
It arrived in about 3 days and took 15 minutes to put in. Back in business.
I hope my experience helps you to figure out your issue.