Thanks for putting all those details in! Exactly what we want to see.
Unfortunately nothing jumps out at me as the smoking gun.
You might try the Beta Drivers for the 4600, you're currently on the latest stable which shouldn't be a problem
https://downloadcenter.intel.com/Detail_Desc.aspx?DwnldID=23985
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Possibly try renaming the Documents PvZ folder, this should reset a lot of settings encase they got changed somehow.
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I'm taken back by your computer hardware though. 4770k with a high end motherboard.. yet no dedicated GPU? It's screaming for one.
Doubt that is the problem though as I can play this game on my mobile HD4000, albeit not very well.
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If the 4770k / RAM is overclocked, save the profile and revert it back to stock.. just to test.. very much doubt it judging by the error but maybe.
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Locatate the PvZ.exe in Origin Games folder, Properties, Compatbility, Run as Admin.. again doubt it
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You may try to contact EA
http://help.ea.com/en/contact-us/new/
Weekdays are your best bet for getting someone. I believe Sunday they also have some hours maybe?
