That belt disintegrated because the compressor is locked up tighter than a whistle. What many people often overlook is when the a/c system leaks refrigerant, it is also leaking out lube oil. They add the refrigerant but dont add any oil and after some years of doing this eventually the whole system lacks sufficient oil charge and the already worn compressor is now running with little to no lube oil and she dies and throws her guts up all in the system. So to fix this system right it is going to need at the very least compressor, drier, condenser coil, oring kit, orifice tube (front), TXV (rear) and some say even new evaporators. It is just so much cheaper to replace a compressor before it dies then all that is needed is just a compressor, drier, oring kit, orifice tube and you are on your way.
My advice to anyone with 200K+(maybe even as low as 150k) on original compressor is to replace before it dies.(If they are planning on driving the vehicle until the frame falls in half or the wheels fall off).