Thank you for your inquiry regarding your iPhone 3G Farid.
The issue with your iPhone 3G going to the iTunes with USB screen mode, is an indication that the upgrade you attempted to perform somehow removed the previous iOS (iPhone Operating System) you were using prior to the upgrade you were attempting achieve.
As a result, you are correct. Because you are connecting your iPhone 3G to another computer, you would not be able to sync with the other computer's iTunes library, without risk of losing all of your media on the iPhone 3G.
To resolve this issue, you would need to attempt to perform a restore back to the factory settings on the computer that contains the iTunes library you have original synced your iPhone 3G with.
This process will wipe the data from your iPhone 3G, yes, but if you have previously synced your iPhone 3G with that iTunes library on the computer in the past, that means the iTunes library will have some previous back ups from those past syncs you have performed with your iTunes library.
If that is the case, then when you perform the factory restore Farid, you will then need to follow up and perform a restore from your most current back up process in iTunes, so you can restore your iPhone 3G back to its most current settings and data, contacts, and pictures.
For a support page reference on how to perform a factory restore and a restore from a previous back up her is a link I would like to provide you for review:
You can also use a software solution if you do want to safely transfer your data from your iPhone 3G to another computer with another iTunes library on another computer if you so choose.
One of the better software titles I recommend is called: Media Widget iPod Transfer Software
This is a great software solution for any iPhone, iPod Touch or iPad product.
Let me know if this helps. If you have more questions regarding this issue or what I have provided,, please free to reply back to this post.