I've repaired my garmin device with the help of one guru.
As I've written before my 2360 was at preboot mode only for 15 seconds and I was afraid of flashing the firmware.
But you can flash it as soon as it is detected by the PC. You just press the upper left corner then updater.exe detects the device and you quickly press OK then updater begins its work and you can stop pressing.
The problem was that cure firmwares didn't help. So that guy has made some firmware which restores the filesystem and it has worked. After that I could restore back my device from the backup.
He assumes that the filesystem has broken because I've connected it to the Linux system.