I think this is the interesting bit, no book symbol showing, it will show if there is no gas in the system.
One thing I would say is have you checked your A/C compressor link lead?? The lead runs from the blue connector just under and forward of the engine bay fusebox down to the compressor. Its a very thin and rubbishy sort of lead and easily damaged...
...this was the lead from my P38. For months I had had intermittent A/C, sometimes it would work and sometimes it wouldn't. Drove me mad looking for the fault, I had replaced nearly every sensor inside the cabin and even replaced the HeVAC ECU itself (the display had gone so it needed doing anyway).
I took it to an A/C specialist who claimed to know about Range Rovers and all that happened was me getting all the plastic fasteners broken that hold the passenger seat base surround in place as they tried searching for the fusebox inside when all I had wanted them to do was tell me whether there was a gas charge in the system - me = not happy.
I spent hours trying to find the problem until I came across a small technical bulletin hidden away in RAVE which described my symptoms down to a tee...
...I immediately went out to the vehicle, started up and turned on the A/C to LO both sides full blast, the engine revs dropped a little and then came back up as they always do as though the compressor was going to kick in but nothing. I opened the bonnet and as I went to check the lead as I grabbed hold of it - CLICK! - the compressor engaged and the A/C blew nice and cold. Ordered a new link lead from the dealer (new part number for the lead is YMQ103910) , cost a fiver, installed it and reliable, constantly working A/C was back - woo!

So, check the lead very carefully, especially at the compressor end, you may just have a dodgy lead like mine. You will need to get your hands dirty to check the lead, you need to snake your hand/arm down past the turbo pipes to reach the connector itself to unplug it.
Let us know how it goes!
-Wills
P.S. The TSB says the the book icon should be showing with this fault but I found that wasn't the case. My book icon never showed and no faults were logged so that part of the TSB is a little bit misleading.