|which also rules out processor getting hot.|
No it doesn't. With BIOS is running and in text mode the processor is not doing very much, barley past tick over.
When t starts to load the OS both the CPU and the graphics suddenly have hell of a lot of work to do. It could still be overheating.
can't get into safe mode for shutting down,
You dsont go into safe mode for shutting down. You go into safe mode at boot up. Safe modes loads a lot less and if you can get into safe mode it can narrow down the possibilities.
To get into safe mode start tapping F8 as soon as Windows begins to load.
I would also run a memory check.