Sounds like Intel HD graphics with old drivers.
https://downloadcenter.intel.com/default.aspx
Check DXDiag and see what you have.
Start -> type: DXDiag -> Save Information
More detailed description = http://answers.ea.com/t5/Titanfall/PC-Graphic-performance-issues-in-Titanfall-here-s-how-to-help-us/m-p/2454360#U2454360
If you have an nVidia card it isn't using it.
http://imgur.com/a/6KJBH#87BGUaE (Replace BF with PvZ)
nVidia Control Panel -> 3D Settings -> Program Settings -> Add Program (PvZ) -> High Performance Processor
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If it just says Intel HD... then it's using the CPU. Depending on which model# the HD graphics is will depend on how good it will play. HD4000 or below.. not so much... 4600 / 5000 / 5100 / 5200 you can probably find a playable level to the game.
moreinfo:
http://answers.ea.com/t5/PvZ-Garden-Warfare-PC/READ-FIRST-Before-making-a-new-topic/m-p/3032830#U3032830
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Refund:
http://help.ea.com/en/article/returns-and-cancellations/
http://help.ea.com/en/refund/
Contact needed:
http://help.ea.com/en/contact-us/new/?product=origin