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I am still confused about what you want. Some possibilities:
1. You want to show the approx capacity left in the battery; how many hours (or days, suit yourself) it is going to live under specified load.
2. You want to tell the user that it is time to replace the battery now; the system cannot run at this voltage.
3. Or just a battery voltage indicator as mentioned in your original post. I presume this voltage is measured under load. I also guess the battery you are using is equipped with standard protection circuit.
4. You do mention that 3.2 to 4.2 the circuit does not operate; not clear to me, why so?
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