There is a list of manuals somewhere on this forum, but the search functionality is rather underwhelming so I cannot find it right now.
I could find this however which is for the 2020 version. Which should still apply now
Do you have any controllers connected to your PC? They might have buttons/controls mapped to things that interfere.
Also make sure you have completed all preflight inspections.
I have just tested this on my PC and CTRL+E did start up the TBM. However it also shut down after a couple of seconds. However, I could start it again using the starter switch on the roof (CTRL+6).
No idea what causes it to shutdown every time.