I see, no PROF_SAVE makes sense I guess if it's never successfully launched, that's when this file gets created.
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I doubt this is the problem but the Lenovo drivers are not current with AMD's
Driver Date/Size: 6/23/2015
vs AMD's 4/4/2016 (hotfix) 3/28/2016 (original release)
http://support.amd.com/en-us/download/mobile?os=Windows%2010%20-%2064
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I was having somewhat a similar problem with another frostbite game recently (computer lockup after 10~20 minutes of play). I tried everything under the sun, fresh install win10, everything possible disabled in BIOS & Device Manager, tried external sound card (suspected sound drivers as it gave me false hope when it wasn't crashing with all sound devices disabled, later turned out to be luck and really didn't help). Nothing was helping. I eventually narrowed it down to PSU or RAM (despite playing for months many other games SC2 and D3 included)... I used HWiNFO64 on a second monitor viewing only the sensors for voltages those looked normal even when it locked. I reduced my RAM's timings a notch and dropped the bandwidth down a notch too, never had a crash since (these were using stock XMP settings and they were not failing under hours of Memtest86 or Prime95 blend).
I'm not suggesting that's your problem but that caught me off guard as a solution to my problem. I doubt a laptop's BIOS even has settings to adjust RAM timings.
Here is this thread where a user has a similar problem. I threw some ideas against the wall but it didn't help him. Maybe it might help you?
http://answers.ea.com/t5/Technical-Issues/Start-freeze/m-p/5283311#U5283311
Clean Booting (I don't think I see that mentioned but that's an easy one to try) // Disabling all the background apps and services that Windows10 runs that aren't needed.
Since you work in IT, perhaps you could try swapping out the RAM with something in your desk as a test.
Run some benchmarks/diagnostic software tests to see if they can recreate it (I couldn't recreate my issue in anything I threw at it though).
I'd personally treat it like the computer is crashing instead of blaming it on the software and work it from that angle.
Since you work in IT throwing a copy of Win7 64 on it (carve out a partition for it) might be something to try. I was about to do this for my issue.
If you've given up hope you can request a refund here:
https://www.origin.com/en-us/great-game-guarantee
http://help.ea.com/en/refund/
Best of luck.