It usually is damaged VGA simply not visible on the chip. I encountered such issue before but the Win 7 logo is flashing and is GPU intensive. Integrated VGA hardly display it with good FPS. I am currently running a Video Memory stress test CE v.1.21 and it appears it doesn't recognize the product version, vendor name and device name yet it shows some weird symbols like crosses and thick vertical lines "|" but 2-3 times thicker and dots between the symbols.
No errors reported so far and 2 passes already completed. I booted Ubuntu later version and it was stable. No video issues so it hardly would be VGA. I played online high quality videos too. The vga on Ubuntu doesn't give a big performance through.
Ubelievable I used Windows 7 instalation cd to start the recovery console from there and reset the MBR/Bootsector and it shut down the same way. Recently I encountered such behavior on another Amilo notebook Pi 2516 or something and it happened to be the heatsink. Not the fan but the Cu(copper) metal transporting the heat. The CPU overheated but not so much hot air was coming out so it was hard to tell what was happening. The computer was shutting down at
-booting os
-booting installation cd/usb installation
-booting even ERD Commander...
-booting Mini XP
Always around the booting logo screen so basiclly at that moment the anti high temperature system was activating or something like that but doesn't seemed to be because of high CPU usage. New heatsink was like maybe 100$ not even with a new fan!
The cpu temperature showed around 60 degrees in Mini XP not having much usage/calculations so it could be overheating. The fan stops from time to time. I flashed the Bios from 1.0A to 1.0H with no change in the issue.
This could hardly be overheating issue having in mind the notebook restarts/turn on itself. Overheat would cause permament shutdown. Some computers even don't allow to be powered on after such event until they cool down.
HDD regenerator finished with no bad sectors. I tried another hdd with the same result. I tried another power adapter (fortron) with 4.74 amperes max so it is very good one. 90 watts total and a lot more than the required ~65 watts. I even removed the hdd so no interface would be used and started win 7 installation from usb hdd with no difference.
The notebook is powering the usb to hdd device even when the notebook is turned off. This could be an issue. Computers ususally don't do that unless there is an option to be waken up by such event like mouse/keyboard button.
The bios only has "wake up from LAN" and it is disabled. I tried the usb hdd device on another notebook when it is off and the diode doesn't light up.
The notebook is working while only on battery.
I removed the lens cables for the cd rom, speakers, touchpad and now the hdd and touchpad no longer blink one after another but only the touchpad diode blinks. Something caused a difference but the shutdown occurs the same way. I removed the upper ram behind the keyboard too while testing.
I reset the bios manually and no difference

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