The battery isn't hard wired, the small PCB the three wires are connected to can be unplugged from the pins sticking out of the case. But it sounds as if this unit might have bigger problems than not restarting.
The yellow banner could indicate a depth sensor failure, for instance, or bad sensor readings being detected. Or a deco violation, depending on the text message in the banner. I can't diagnose from a distance, but the symptoms you describe could be consistent with a leak letting water in at the HP end, or a sensor failure.
You don't say how old this Cobalt is, or what the message was on the screen. If it's a Cobalt 1 the Back and Select buttons don't generate a reset.
If you can try a reset by unplugging and re-inserting the battery you might be able to see the log- however if it did not complete the dive you would see only dashes.
Sorry this happened on a trip, it sounds as if this Cobalt needs to go back to Atomic for service. I would suggest contacting Adan there for a return authorization,
adan.campos@huishoutdoors.com. They are very good about this sort of thing.
Ron