'System software missing' message is indicative of a failed software upgrade. The firmware has perhaps been erased from the unit but the process has failed or been interrupted at that point and new fw hasn't loaded in other words. The unit may not even need to be 'cured' in the sense that it maybe isn't really bricked. Try reloading the V3.90 EU fw [original not cure], there are several possible ways to perhaps achieve that. Try these turn, moving to the next if not successful:
1. Connect to PC and drag nuvi16xxEU_regionfileonly__390.gcd onto the WebUpdater shortcut or directly to WebUpdater.exe in the Garmin program folder.
2. Convert the nuvi16xxEU_regionfileonly__300.gcd to 113201000.390.rgn using RGN_tool. Then connect in pre-boot and flash the rgn with Updater.exe [try this repeatedly, even if it shows the 'unable to program the requested memory region' repeatedly].
3. Rename nuvi16xxEU_regionfileonly__300.gcd to gupdate.gcd, place in a root folder named Garmin on a microSD. Have the unit fully off [force it off by holding the power button if needed], insert the card and turn the unit on.
These's a fourth method too, involving kunix's method of modding ldr.bin and flashing via Updater.exe to execute txt on microSD to delete the existing [perhaps corrupt] gupdate.exe from .System folder by overwriting it with a known-good file. If none of the above 3 work, i can make a kit for you to try that too.