2004 Fuji Royale hybrid, rusty: to restore or not?

Hello everybody. Got a present: 2004 Fuji Royale hybrid. It sat on a Brooklyn balkony for about 7 years (!) completely neglected. That's a 19.9 lbs, 27 speed bike with carbon fork and rear Ultegra. Its very rusty. Frame is aluminum so its good. At the very least it will need new chain, cables, rear...