Look at the motor, if it says 36v on it, it is definitely worth $350 if it runs when a 12v battery is hooked to the wires. 24v ones are worth about $250. Your guess is good as mine on the value of the frame, but it is a pretty nice frame for an ebike in my opinion. I'd say frame alone is worth $100 to someone who is into ebikes. If there is no controller, just get one from ecrazyman or a scooter place. A 15-20 amp brushed is all you need, and a throttle.
On the battery, is the battery case even still there? If so, it has sla's inside it, and a built in charger. So you just open it up, and get some more sla's in the same size from b&b or some other reputable source. On my bike, I'm replacing the sla with nicads from ebikes-ca. The hole for the battery will fit a 36v 8ah pretty nice. I'll be carrying one 8 ah 24v pack in the frame, and another on a rear rack parallel connected so I'll have 16 ah of 24v. I'll have the same weight and double the range.
I really like mine, but at 24v it is a bit weak on the hills. Overvolting a 24v can be done, but I fried one that way last winter. At 36v on a 24v motor, you need to keep the rides real short. But the frame is great, and like I'm trying to, selling the motor so you can put a faster one on is a possiblility.