Why wont iTunes let me add music to my iPhone?

Well I had just recently got a new computer (a Mac) since my old one (a Dell) died. I used iTunes on my old dell for awhile (3 years) and when i switched i was unable to really get anything off from my old computer due to my harddrive being completely unrepairable. When i went to go and plug in my iPhone into my Mac it would synch but only my notes and safari safe browsing data and thats it. I would try to add a song like the usual way you would (add it to your iTunes library then add it to your phones library) and it will not go over. I am confused on how to fix this. Any advice?

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.
http://ipodiphoneipadcopytools.posterous.com/ipodiphoneipad-to-mac-transfer