I have archos 504 160 gb when it turn on i have message (recovery code 4) would you like to recover your system ? no - repair disk - format disk when i push no no thing action . when push repair or format these message appear ( connect your device to your pc and install an update file) please help me

From Archos' support website FAQ:

When I switch on my Archos device, the following message is displayed: "Would you like to recover your system?" What does it mean and what should I do?

You are on the recovery mode screen. It means that your hard drive has been damaged and must be repaired or formatted.
With this system recovery mode, you will have to select between "Repair Disk" and "Format Disk".
Start by selecting "Repair Disk" and follow the instructions displayed on the screen. See the full PDF manual (available on the Archos web site) on how to use the Repair and Format options.

If repairing the disk did not work, try formatting the disk by selecting "Format Disk". Note that the formatting will erase all data.

If you still cannot restart your Archos after trying a system recovery, you should contact Archos technical support.

http://www.archos.com/support/support_tech/faqs/en/faq_Archos405.html?country=us&lang=en

when i turn it on it goes to a white screen with a blue line across on the very top it says recovery code 108 the next line says "would you like to recover your system?" then it gives me three options no, repair disk, and format disk. I dont know what to do cam body help me?

If you chose any of these options already your Os is gone.. 
try this solution 
I fixed my son's 605 4 GB had Recovery code (104) on it. This might work for other error codes too. These are the steps i followed 
* Use the computer for this process that you always used for this archos Archos should be plugged in to Pc before starting the process.
* Download the firware Upgrade 2.1
* Plug the Archos to Pc 
* When the white option screen comes up pick the format disk
* Wait until all done do not pick any option on archos after format is done Pc should recognize your archos in 5 seconds 
* Put the firmware in root section of the archos not in any folder.
* Safely remove the usb for Archos from your pc first and then unplug the cable.
* Do not pick any option on the Archos screen
* Just turn it off from the power button by holding it until it turns off
* Wait about 5 minutes and plug it back to pc 
* it will come up with white screen again but this time it will start Update you will see the progress bar moving, wait until it is all done, it will shut off. Turn it back on and  your archos will be back to normal

I hard tried the same thing to transfer a 6.7GB file to another computer.I had formated the drive as an NTFS drive. when i turned archos back on, it failed to turn on give me error code. but for some reason it asked me to do a recovery. I remember i had seen some recovery files in my archos device saved (zipped file packages). And when it was doing the recovery i noticed it was reading the zipped files for recovery purpose. After the recovery, i did not see the files anymore in the device. So if i do the same thing again (format as ntfs) i might not be able to recover it back again.

recovery code 102 screen - this error message means the the hard disk has failed - I am guessing that the unit has been dropped at some point - Sorry but it back to Archos - The UK number is 0207 949 0115

Recovert code 104
would you like to recover your system?
NO
Repair disk
Format disk
P.S. pressed the OK button on the device and its telling me to
connectto your divise to my PC and install an update file DONE
then the devise reapear back to recovery code 104

go to archos firmware and download version 2.1.04 to your pc or laptop and save it in a folder then get ur mp4 turn it on and go format you will get a screen that says done leave it on that and connect to your pc or laptop it will recognise your mp4 then go in my computer and open 405 and open your save file and drag the save file into the 405 but NOT into a folder below them and after it has\copied turn the 405 off and start it up should be as good as new

install the file from the folder where you have saved this file.and it should work.

Carbon Adsorption Solvent Recovery Systems

it sounds like the partition that hold the recovery files has got damaged,i suggest you talk to the manufacturer or supplier on how to overcome this problem,if it was a pc i would say format hard drive & re-install the software but its not .
good luck
Terry