screen distorts and computer shuts down
t430 screen distorts and then computer shuts down
could be heat related. Let us know in what manner the screen distorts. Attach an external monitor and see if it does the same thing. If so you want to check your airflow and temperature of your processor etc. Could be a GPU issue.
You did not make any mention about it functioning properly in Safe mode. That is new information that you did not make immediately available. Yes, it would. If it works in safe mode it is most likely software related (could be hardware since safe mode does not carry the higher resolution) as well as this "bootmgr image is corrupt. System can't boot" so I can't even get to safe mode." being a good indication of that. I suggest a clean install of your OS as well as the drivers.
Video drivers, in my experience, can produce all kinds of strange errors.
If you can boot up in ‘Safe Mode’ try uninstalling the video driver and let it re-boot to Microsft’s generic driver and work from there.
Yes would agree that a heat issue would still occur in ‘safe mode’ but….you never know.
There are many causes of boot errors. Corruption, failing drive, etc. Is it still not booting in ‘Safe Mode’?
Can you make a USB boot drive with Windows installation and attempt the boot repairs?
Let us know how it goes.