Device isn't eligible for the requested build - Stuck in recovery mode

This support document provides help with being unable to update or restore your iPhone, as well as information on recovery mode. If you can't update or restore your iOS device

However, this support document has information about the error you indicate. Error 3194, Error 17, or "This device isn't eligible for the requested build" This generally comes from trying to put the wrong iOS on a device, or jailbreaking. I see you mention not jailbreaking, but it is interesting that you attempt to modify the hosts file. Have you used that computer to jailbreak a device before?

Try the troubleshooting tips in the support documents that I sent to you.

paulfromfrance wrote:

This computer has never been used to jailbreak any device, but I saw an article on the french apple website telling me to add a "#" in front of the gs.apple.com hosts, wich I did but it didn't change anything.

If there was a gs.apple.com entry in the host file, then that computer WAS used to jailbreak, or attempt to jailbreak an iOS device. There is NO other reason for that entry to be placed in the host file other than in an attempt to bypass Apple's authentication servers.

Make an appointment at the genius bar of your local Apple Store since you can't seem to find a 'clean' computer from which to perform the restore.

Ask the genius to restore your phone. It's still under warranty. If there is something wrong with it, it will be replaced.

If the links Chris provided at the very beginning of this thread didn't help, then there isn't much more we can offer other than to tell you to have it looked at.

If you attempted the restore on a virgin pc with a fresh install of the current version of iTunes and you still got that error, then there's probably something else that has to be dealt with.

If you can't make it to an Apple Store, call Apple. Your phone is still under warranty.

Manually selecting an ISPW is not the way to go. That will just compound your problems. You would not get the correct file. You connect the device to iTunes and then restore from there. The 3004 error is discussed in the second link I gave you. Try putting the device into Recovery mode as indicated in the first link I provided you and see how it goes. Otherwise, you will need to make an appointment at the Genius Bar as KiltedTim indicated.

paulfromfrance wrote:

This computer has never been used to jailbreak any device, but I saw an article on the french apple website telling me to add a "#" in front of the gs.apple.com hosts, wich I did but it didn't change anything.

The ONLY reason there would be a line containing gs.apple.com in your hosts file is if the computer was used in the past to hack or or jailbreak an iOS device. There's no other way gs.apple.com would ever be in your hosts file. If you didn't jailbreak, did you ever use another hacking tool like tinyumbrella or recboot?