Syncing to an empty address book will erase your contacts on the phone, especially if you connect to a new computer. You'll have to restore your phone from a backup from the time before you switched the PC.
More info mentioned in this user tip here:
Thanks. I still have access to my old computer with the older backup.
What should I do?
If I connect my iPhone to my old computer, it will sync and all my contacts will disappear also on old laptop?
What are the steps to avoid this?
And what should I do afterwards to avoid loosing my contacts again after connecting to my new computer?
Contact info is part of the backup, see if you can replace the backup folder on your new computer.
The location of the backup folder is mentioned here:
The folder where your backup data are stored varies depending on the computer's operating system. Make sure the backup folder is included in your periodic data-backup routine.
iTunes places the backup files in the following places:
- Mac: ~/Library/Application Support/MobileSync/Backup/
- Windows XP: \Documents and Settings\(username)\Application Data\Apple Computer\MobileSync\Backup\
Note: To quickly access the Application Data folder, click Start, and choose Run. Type %appdata% and clickOK.
- Windows Vista and Windows 7: \Users\(username)\AppData\Roaming\Apple Computer\MobileSync\Backup\
Note: To quickly access the AppData folder, click Start. In the search bar, type %appdata% and press theReturn key.
copied from iTunes: About iOS backups
You could try to copy that whole folder to your new computer and replace the existing one. After that check if the backup shows up in iTunes/Edit/Preferences/Devices. If yes, use it to restore from and all your info should be back on your phone.
For information about how to create and restore from a backup, see iOS: How to back up.