ITunes Computer Authorization

Ok, so here's my problem, i have an iTunes account of which my iPhone is synced to, i can't download songs onto it from any other account. The account that my iPhone is synced to is already authorized on the maximum machines it's allowed to be on. My desktop, my laptop, my sisters laptop, the family desktop, and finally my dad's laptop. The only problem is, my laptop was recently stolen. And that was one of the devices that the account was authorized on, and i have reached the maximum devices, so when i bought a replacement laptop, i can't authorize it for downloads. Is there any way i can get my phone to sync to a completely new account, and transfer the songs and apps from the previous account?

-One thing, i can't de-authorize any of the other computers because my family needs them for their devices.

It sounds like you can de-authorize your old laptop that was stolen and authorize the new one. You can do the de-authorize from any of the other authorized computers. If you can't do this or don't want to do this then no, you are not going to be able to get to your stuff. Apple is really strict on how many authorized devices you can have.