Windows 7 (Vista too): shutdown and power on again, almost like a reboot but not exactly

Hello to everyone! :D I am writing in the hope of finding a solution to a serious problem I'm experiencing, certainly not tied to a software problem but one that I hope we can find a work around by software.
My laptop (an HP DV3-2350EL i3 330m cpu and ATI Radeon HD4550 discrete graphics) has problems with shutdown. Under Linux it shuts down smoothly both on AC and on battery power while under Windows 7 (both on 32bit Professional and 64bit Home Premium, Vista Business tried too with the same outcome) it shuts down fine only on battery power while connected to the AC power it shuts down fine but after a second it turns itself on again (not exactly a reboot because in case of a reboot the LEDs are always lit while in this case the LEDs go off for a second and then turn back on just as if the laptop shuts down to turn on again soon after by itself.
Another strange thing is that, right after finishing to install Windows 7 BUT ONLY FOR THE FIRST TIME EVER, and without installing drivers or anything, literally anything at all, I can also safely shut down the laptop from the mains but never after that time.
Since the laptop shuts down fine ONLY at the first boot after installing Windows, I decided to create a restore point IMMEDIATELY: incredible but true, even restoring that state, nothing to do, even right after the end of the restore process the system can't no longer be shut down properly. I think this once again gives evidence to the hypothesis that the problem is not software.
Another equally strange thing is that, if I update the bios (already done it to the latest version to no avail), when the update is finished (the update being made under Windows) the update tool takes control to turn the laptop off and in this case is successful. The bios is an Insyde as of course the upgrade program.
I should point out that before posting my problem here I have done extensive research and tried different solutions:

1) Changed the registry key Winlogon PowerOffAfterShutdown bringing it to 1
2) Checked the event log: nothing abnormal except for an error with WMI solved by a Microsoft Fixit and a warning for the LMS service of the Intel MEI (error present on all my pc's based on i3 and i5 cpu's I therefore do not consider relevant)
3) Confirm whether there are devices that can wake up the system with the command powercfg-devicequery wake_armed (no device is enabled to do it)
4) Updated all drivers to latest versions available
5) Tried turning off 'manually' using the command shutdown-s-f-t 0 without results: I didn't expected anything different than that since it is essentially the same thing done in a different way
6) Disabled reboot in case of serious problems during shutdown

Although, if it had been, in step 3 I had to get different results:

7) Checked the options belonging to wake-up in the bios (there are none, the bios is very basic and allows virtually no configuration)
8) Checked all the advanced settings of the network adapters via device manager: no device is enabled to wake up the system
9) Tried also to disable energy saving by selecting the maximum performance profile but still nothing. The same happens reproducing the same profile of battery power (integrated card instead of the discrete, etc.)

The system is absolutely stable but to turn it off I need to 'restart' it (the quotation marks are due according to what already explained), interrupt the boot with F8 and keep pressed the power button.
I emphasize that even from there, if I press the button briefly as it should be sufficient, the PC will come on again after only a second.
I am reasonably sure it is not a software problem but an hardware one. I underline again that under Linux the laptop shuts down fine both on battery and AC power. It happens under Windows too if the signal is sent off from the bios update tool and the both of these evidences make me believe that the management of power states by Linux is different and gives me hope that even under Windows 7 the shutdown process can be managed differently (like it seems to do the bios update tool) so as to properly power down the laptop.
True, it wouldn't solve the problem but if I could get around it then it's fine for me! ;) Thanks in advance to anyone able to help me.

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