mmmm... Do any other games cause you problems? If you don't have any others you can maybe use a Benchmark tool like Furmark to test.
shcore.dll shcore.lib..... I can't seem to find any related crashes for anybody on google on any game or app really.... I'm basically guessing these have something to do with graphics in windows going by google results.
... If it fails other games/benchmarks. Maybe double check that the power supply is properly connected to the 970, nothing came loose or anything like that.
------------------
When the game loads then crashes. Afterwards does it create a new Documents folder for PVZGW2? Possibly you can try forcing borderless mode or something.
edit with notepad.
\settings\PROF_SAVE_profile
Borderless:
GstRender.FullscreenMode 2
GstRender.FullscreenScreen 1
-----------------------------
You may contact EA here because I'm not coming up with anything solid anymore.
https://help.ea.com/en/contact-us/new/
*please let us know if you manage to solve it and how.