Your question is at best hypothetical. If you really plan a dive at night, under ice, by yourself this way, God be with you! I have been a professional diver and gone to places some people would not dangle their feet in, let alone dive in (like sewer outfalls) zero vis, even with lights - and let me tell you, your plan of going down solo, at night, in an overhead environment only with a rope tied around your waist is asking for trouble. At least they'll be able to retrieve your body easily. First of all, you would have a stationary down line (weighted, with a strobe attached) to help you ascend safely, if your computer failed. (I'd even insist on a spare tank and regs attached to the downline, with yet another strobe). Secondly, You'd put fresh batteries in your computer no matter what, and carry a set of analog (mechanical) gages, just in case - I don't trust anything with batteries. Thirdly, in my line of work we were required to have a stand-by diver, fully dressed-in on deck if we dove in an overhead enviornment alone. I'm a solo diver. Always have been, always will be, and the only thing I fear under water is another diver. I am my own best redundancy. No gadget, nor ill-trained amateur buddy is going to be my insurance for a safe return. Neither is the dive tender who may or may not be paying attention (was that three pulls or four??) It's all up to me and me alone. Dive safe. It's your life.
