The damage caused by a failing component can be profound - and extend well beyond that individual component (a short especially, can affect many things). I doubt that removal of the B2B Button will make any difference at all - but feel free to try anything you want; I understand that replacing this board will be costly.
No, there is no option to ignore the B2B button. It is a recovery capability that is supposed to override any BIOS Settings.
In regard to your concern for the "Back to BIOS", please refer to the following thread: https://communities.intel.com/thread/31839. There you will be able to find some information that may come in handy for you.
In regard to the smoke, please try with your equipment "turn off " try to see if there seems to be any part burn or different.
Also if you have a chance please try to run the Intel® Processor Diagnostic Tool.
Please let me know how it goes.
Hope I can hear from you soon.
Well, yesterday i was able to update the bios version of that computer to the latest (650), although i already had updated to this bios version a long time ago before this problem occurred. I did that just to check if it would make any difference but it didn't, the computer still doesn't try to load any OS because it thinks the B2B button is pressed, and it isn't. I'm not even using the shield (aluminum plate) so the button is not stuck and is not red.
I should note that before that i tried to update the bios by using the BIO file on a cd on an external usb dvd-drive because i don't have an internal dvd-drive, and was not able to do that when pressing F7 on boot, because the external dvd-drive was not recognized on the F7 bios recovery procedure. Yesterday i was able to update the bios using an usb thumb drive, so that means the F7 recovery procedure works with the usb thumb drive, probably works with an internal dvd-drive BUT doesn't work with an EXTERNAL dvd-drive. I think Intel could improve on that procedure if possible. That is also applicable to the procedure of changing the CMOS jumper to the configuration position or just taking the jumper out.
About the Intel Processor Diagnostic Tool, i'm not able to use it because that computer doesn't load any OS and i don't have any other compatible mobo for my I7 3930...