Unable to restore iPhone 3GS backup on iPhone 5S on new PC

Similiar problem here, backed up old working iPhone 3GS (iOS 4.0) to iTunes (latest version of 11), bought New iPhone 5s (iOS 7.0.2 then updated to 7.0.3) from the Mac Superstore, much to my suprize they would not transfer data from old working iPhone to new purchased iPhone, but instructed me to go home ad make transfer from iTunes, I then tried to install the iPhone 3GS backup onto the new 5s from iTunes and repeatedly get a message that an "error had occured" with no error code. Have spent several hours trying to resolve, including considerable time on Apple Care were I was ultimately transfered to senior tech support person, we then ran out of time. Apple Care seemed puzzled about the error message not having an error code.

Get to try tech support again tonight, if I don't take the 5s back first and give up the new iPhones first. I have never had problems transfering information on any cell phone or iPhone before.

Just tried several things from step 4 below, with Firewall/Antivirus software step. Included uninstalling Norton since it had just expired, and installed new McAfee Anti Virus Plus 2013 with latest updates, still no luck. Still get the "iTunes could not restore the iPhone "Name" because an error occured" (no error code) VERY FRUSTRATING!! Did manage to get apps uploaded from iTunes but only the apps, no photos, text, address book contacts etc. when the firewall was turned off.

http://support.apple.com/kb/TS2529

1. Back up your backup

2. Update to the latest software

3. Disconnect other USB devices

4. Check security settings

Most backup issues are caused by out-of-date or incorrectly configured security software and firewalls. Disabling security software is unlikely to turn off the security process that is interfering with the backup. You may need to temporarily uninstall third-party security software to back up your iOS device if the most recent version of that security software hasn't been updated since the latest iTunes release. After backing up and syncing your iOS device, reinstall and set up compatible security software.

You must update and properly configure security software and utilities manufactured by companies other than Apple (third-party) to effectively protect your computer while still allowing iTunes to communicate with the iOS device. If you have updated iTunes since checking for security software updates, your security software may be out of date.

5. Back up using a new user account

6. Reset the Lockdown folder

7. Back up on a different computer

What APPEARS TO BE THE ANSWER - iPhone 3GS (iOS 4.0) is not compatable even via iTunes with iPhone 5s. Got some apple staff to admit this is likely the real problem (at least through a PC, unknown if better chances through a Mac), but will not be the official answer. Could have saved 8 hours of frustration. They copied address book from old phone to new phone, everything elese needs to be manually done, and apps can be selected from app store on iTunes, photos treated like moving from any digital camera, and text are just gone.

If you have the old phone, plug that in first and make a backup, that way you will have all the latest info.
Then plug in your new iPhone and when asked if you want to set ot up as a new phone or restore from a backup, make sure you select restore from back, then you can pick the backup you want to use, select the latest and away it goes. If you have the old phone, plug that in first and make a backup, that way you will have all the latest info.
Then plug in your new iPhone and when asked if you want to set ot up as a new phone or restore from a backup, make sure you select restore from back, then you can pick the backup you want to use, select the latest and away it goes.

More Reviews:
How to transfer iPhone contacts to Computer
How to transfer iPhone contacts to iPhone