If putting a new battery in it didn't solve the issue then I would guess it's a heat issue. Maybe it has a heatsink that has come away from / no longer properly seated on the processing chip and is causing it to reboot? That would be a typical PC scenario as many processors have thermal protection built in and will simply reboot when the pc hits desktop due to thermal overload if the thermal compound has come away or become loosened allowing air underneath, as booting itself is CPU and thus heat intensive.
Wondering if it got knocked or dropped or just handled roughly and if this could have caused any heat sink separation?
It's very difficult to guess not knowing the internal layout of the individual cam and whether or not it requires / has heatsinking. However, if you previously fitted a new battery, that really rules out a battery issue. BTW a flat battery after a year of storage is not unusual. Batteries discharge slowly over time without use. That's perfectly normal.
Another guess might be the breakdown of some sort of voltage regulator allowing over voltage / heat.
However, at the end of the day, these are just guesses. You'll only really know if someone with the correct knowledge can get inside and analyse it. That would probably be the manufacturer and something that would cost far more than the cam is worth in postage alone.
I think my advice would be leave well alone - be careful with lithium batteries as they can explode if not charged at the correct rate. Might be better to simply move on and buy a better solution and write the brand off to experience.