Sadly no response to your question indicates that either no one owns such a unit, or those that do are understandably hesitant about dismantling an expensive product.
Unused connectors inside thermal cameras are not unusual. Such connectors are usually for optional modules such as Bluetooth so it is worth looking for models higher in the same series to see what they have and yours does not. Such 'unused' sockets are often used during the manufacturing and calibration process.
In your position, I would look at the power supply circuits first to establish whether all supplies are present and correct. No power rails = no boot. If all power rails are present and correct on the chipset, move onto how the power button acts on the system. Most likely a soft button requiring that the micro is in a sleep mode. Check the input to the micro to ensure the power button is actually working. Also monitor current consumption when off and when power button pressed.
In my experience on FLIR PM series cameras, the firmware carries out a self test of all elements of the system, just like a PC. If there is no life at all on the micro then self test will not be running and cannot be halting the boot. If you have a functioning micro connected to functioning RAM and ROM, you shoudl see activity on the memory bus. If you have a major fault it may try to boot and then haly but there should have been signs of life on the busses before the halt. No activity at all on any address or data lines points to power supply issues or the reset circuit failing. Dare I suggest that you place an AM radio receiver (set to LW or MW) close to the PCB and try to switch the camera on........ Its crude but I am an RF tech, so use this method as a quick and dirty way to hear activity within an embedded computer system.....they usually make all manner of RF noises when running ! Don't forget to check whether the master oscillator and any subordinate clocks are running. No clock, no activity.
It is worth knowing the history of such a unit as well. Did it just stop working whilst in use ? Did it stop working after a firmware ugrade or hack attempt ? Did it show any signs of failure before complete failure to boot ? Noise on screen from failing power supply etc. Was it dropped ? (that is not uncommon) Look for impact damage on the case. Like Sherlock Holmes, it sometimes pays to consider all evidence before deciding upon a strategy with which to move forwards.
Map out what is, and what is not, showing signs of life in the camera. It may lead you to a conclusion on the likely cause. I have even had equipment fail to boot due to a damaged battery conector or power socket. Nice simple faults like that are a joy, if less of a challenge.
See how you get on and come back to this thread with your findings.
P.S. I use a thermal camera to look at such PCB's for signs of life on what appears a dead board....it can reeal all manner of nasties, like shorts, knackerd capacitors etc. In your case a 'chicken and egg situation unlss you can borrow another thermal camera ?