For your info, if u sync the ip4 at ur office and if u have already backup all ur stuff at your home pc only, all ur iphone apps, videos, songs will be deleted.
If u want to sync the iphone 4 at ur office without losing ur apps, you can do manual to like copy the whole itunes folder from the My Music folder and copy to your office My Music folder to replace it and make sure u have install the iTunes at your office pc first. Den you sync the ip4 at your office pc and the apps will still be there. This is my manual way of doing it and if there is other member's have other way to do it, please share if u have. thanks.

What i do is disable auto sync then choose "transfer purchase to pc"..All the apps will be sync to the pc.

Havent tried for songs though...

for your backup, it depends on whether you backup folder was also deleted. read this here iPhone Backup Location and if it's still there, you might only need to reinstall iTunes. For your apps - just do transfer purchases. THEN ONLY, you may sync your iphone.

is it a fresh install or an upgrade? you're toast if it's the former.

You didnt answer my question dude.

But if youre saying that you wanna sync ur iphone to a new pc now, uve gotta do some trivial things like transferring ur apps, data, contacts and other contents to your new pc before syncing.

If however, you're still on the same machine that got upgraded; have a look at the backup location to see if it's still there coz u can then just restore from backup. (this obviously cant be done if it was a fresh install obviously)

I'm sorry, but i dont really get what you're saying in the first place, but i hope that helps