Ok there's still hope for recovery because you've found occasionally 'System' message shows for 2 or 3 seconds. In that brief time it IS in preboot which is solely when you can initiate a flash - it seems you do fully understand that.

The basic problem of course is that it's 'bootlooping' (i.e. it'll keep powering on/off endlessly as long as the battery can supply power). Additionally, and most unfortunately, your device isn't forced fully off when you hold the power button down (many bootlooping devices can in fact be successfully forced off like that). However despite that problem there are still a few options to try:
  1. Keep trying to 'catch' preboot by fluking an initiation of the cure fw flash. That means following the same procedure i gave but of course without using the power button, i.e. having the fw loaded to Updater with a cable connected to PC, holding the screen then connecting the cable to the nuvi to hopefully initiate preboot at some point (watching the GUI of Updater until you see the device details appear in the window next to "USB Device", at the same time "System" will be showing briefly on the nuvi's screen) then INSTANTLY clicking OK or hitting Enter key to start the flash. You may even have to try removing and reapplying your hold on the screen constantly and/or connecting and disconnecting the cable to the nuvi's port every time in sequence with it powering down and up until you see it's in preboot. Having more that two hands is advantageous with flashing a stubbornly bootlooping device so if you have someone to help with that, use them. Otherwise i've resorted to hitting the Enter key with my right elbow to catch a stubborn device in preboot when cable must be connected/disconnected sequentially.
  2. Leave it sit bootlooping until the battery completely exhausts itself and the nuvi will no long turn on with the power button. That will give you one clear shot at the flash because it should, hopefully, go straight to preboot when you hold the screen and plug the (PC connected) USB cable into it which will then power it on. Again you must have fw loaded to Updater etc. and be VERY fast in initiating the flash as you'll only have a couple of seconds or it'll exit preboot and just bootloop again.
  3. Open the device (here's a youtube [Only registered and activated users can see links. ]) and disconnect the battery entirely. In many Garmin devices the battery isn't an essential part of the electrical circuit therefore you can still power it on from the 5V in USB cable. If it can be powered without the battery in the circuit that will give you a better chance to catch preboot.

Good luck and i'm very sorry for accusing a Scot of being a Pom. I'll practice giving myself Glasgow Kisses in the mirror until i learn my lesson (i already know where the Hospital is thanks) .