Hello people!
Sorry my bad English, but I hope it's understandable.

Here is a description of the problems encountered. I hope it is sufficiently precise to be able to make a diagnosis.

I stored the DJI Inspire 1 pro last June 21 perfectly working.
When I went to resume it, after 9 months, the batteries were both gone.
I bought two more batteries (350 €)!
When I got the batteries, I loaded them and I tried to use the Inspire 1 pro, but the video signal was not displayed on the ipad and the DJI GO App showed a "NO SIGNAL" alert.

To test if the problem is in the app or in the iPad, I connected an external HDMI monitor to the RC and I found that the video signal was not even displayed on this monitor.
I have also tried using an iPhone 6, but without success.

Below the data.

Apple iPad Air 2 16 Gb (Mod. MGGX2TY / A)
IOS 9.2.1
DJI GO App version: 2.7.1
AC firmware version: 1.7.00.90+
RC firmware version: 1.5.80
Camera firmware version: 1.4.0.70

The signal levels indicated by the DJI GO app are maximum:

RC level: 5 bar
HD level: 5 bar

The aircraft responds regularly to RC commands
The X5 camera responds regularly to RC commands
The X5 camera responds regularly to the DJI GO App commands
The X5 camera regularly records photos and videos on the microSd

So I thought the problem was caused by batteries that maybe have a  recent firmware, not aligned with the firmware of the aircraft.

So I tried to update the firmware of the plane:
1. I downloaded the right firmware (for x5) with a PC
2. I formatted the microSd with the plane
3. I copied the .bin file on microSd card from PC
4. I inserted the microSd card into the x5 camera
5. I turned on only the plane (RC is off)

The camera LED blinked red and green alternately for about 10 minutes, then turned solid red and the aircraft issued a dddddddddd sound.
I read the WM610_FC550_FW_RESULT_AB.txt file: the result is failed!

I tried again. The room LED blinked red and green alternately for 2 minutes, then turned solid red and the aircraft sounded dddddddddd.
I read WM610_FC550_FW_RESULT_AB.txt: the result is failed!

I tried again. And again. And again. Always failed! But… the DjiGo App says the plane is upgraded to firmware 01.10.01.40.

I hope you can help me.

First update the go app to the latest  version. I think it is 3.1.10 and make sure you load it for the Inspire 1 and Phantom 3 Advanced or Pro .  do Not load the Go app 4 , that is for the Inspire 2 .  

Does the Result say"failed" and then below it say the "Firmware is the same or older than what is currently on the aircraft" . If you already have the update on the Aircraft then that is what it would say .  

It looks to me like you have the aircraft updated but NOT the camera ,  if you are on version 1.5.8 on the RC then you must update that as well.  You will want to be sure the AC is off when updating transmitter, be sure to have a solid wi fi connection  to the Go app device as well .  
Are you using the X5 to load the latest FW  to the system , You are not using an X3 are you .  

You have the wrong FW on the Camera for sure .  Go to the X5 camera downloads page and download the FW there ,  go to the link below  for the X5 camera , then go to the Downloads tab,  from there download  the file and install like normal to the SD card .  Be sure to use the X5 camera for the install .
http://www.dji.com/zenmuse-x5
So threee things

1-Update go app

2- Update the RC transmitter

3- Update the Camera

donnie

Thank you Dolly.
I'm trying to follow your advice.

But the Result file after "failed" says "Reboot the aircraft and try to upgrade the firmware again."

This is the full text of the WM610_FC550_FW_RESULT_AB.txt file :

Result: Failed.
Reboot the aircraft and try to upgrade the firmware again.

========== 2014.01.01 00:00:12 remo-con disconnect======
Packet: WM610_FC550_FW_V01.00.00.30_gimb.bin
Upgrading ...
Result: Failed.
Reboot the aircraft and try to upgrade the firmware again.

========== 2015.11.08 10:10:09 =====================
Packet: WM610_FC550_FW_V01.00.00.30_1012.bin
Result: Abort.
The firmware on the SD card is identical to or older than the current firmware on the aircraft.

========== 2014.01.01 00:00:12 remo-con disconnect======
Packet: WM610_FC550_FW_V01.04.00.70.bin
Upgrading ...
Result: Success.

========== 2014.01.01 00:00:12 remo-con disconnect======
Packet: WM610_FC550_FW_V01.04.00.70.bin
Upgrading ...
Result: Success.

========== 2014.01.01 00:00:13 remo-con disconnect======
Packet: WM610_FC550_FW_V01.10.01.40.bin
Upgrading ...
Result: Failed.
Reboot the aircraft and try to upgrade the firmware again.

========== 2014.01.01 00:00:07 remo-con disconnect======
Packet: WM610_FC550_FW_V01.10.01.40.bin
Result: Failed.
Reboot the aircraft and try to upgrade the firmware again.

========== 2014.01.01 00:00:06 remo-con disconnect======
Packet: WM610_FC550_FW_V01.10.01.40.bin
Result: Failed.
Reboot the aircraft and try to upgrade the firmware again.

========== 2014.01.01 00:00:06 remo-con disconnect======
Packet: WM610_FC550_FW_V01.10.01.40.bin
Result: Failed.
Reboot the aircraft and try to upgrade the firmware again.

========== 2014.01.01 00:00:06 remo-con disconnect======
Packet: WM610_FC550_FW_V01.10.01.40.bin
Result: Failed.
Reboot the aircraft and try to upgrade the firmware again.