Can I sync iPhone on another computer/iTunes?

My computer wants to be a butthead about iTunes so I'm incapable of using it on my laptop. If I tried syncing with the family desktop, would I be able to access my account and everything so I can back the phone up? Or does it only work on a single computer? (Like my parents tell me)

Added (1). I've tried numerous times to reinstall itunes and its drivers, actually U___U It always tells me the installation of the really important drivers failed.

No they're telling lies to you they probably have some hidden pictures 18+ of them on the family desktop and don't want you to find them, but seriously you can I did it without a problem.

You may backup the device to another computer, however it can only be synced with one iTunes library at a time. You can access your account on the other PC, but your data (music, videos, pictures in particular) won't be available unless it was purchased on iTunes, so you'd have to recover them from your laptops hard drive and put them in the iTunes library on the other PC. I would try reinstalling iTunes and the Apple Mobile device drivers first to see if they're the culprit on your laptop before you consider syncing with the other PC though.

An iPhone can be synced with only one iTunes account at a time.once you switched to a new iTunes account or a new computer. You have to authorize your iPhone to it at first, then you can upload music and video from the new iTunes to your iPhone. But this way will overwrite the original files on iPhone with the new iTunes. You may try this iPhone transfer, it can help you copy files from iPhone to computer for backup, you can also use it as an iTunes alternative to upload music and video. It will not erase your original iPhone files. It's safe and works pretty well for me.