I have a couple of older games that refuse to run on my new machine. They are ArmA 1 and Mass Effect 1. When I start them, I immediately get a popup with

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MassEffect.exe - Application Error
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The application was unable to start correctly (0xc000007b). Click OK to close the application. 
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OK   
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I have done ALL of the usually recommended things for this error. Running as administrator, running in compatibility mode, Reinstalling Visual C redistributables (all years), directX, OpenAl, .NET, etc etc. The problem is that I feel like I'm stumbling around in the dark feeling for a solution, and installing a bunch of stuff I probably don't need in the process. So is there a more technical way to get to the bottom of this error? Is there a way to, say, see that the process tried to use a certain dll and it hung up there or something? Basically I need a clue as to what is going wrong.

I'm on Win 7 x64 with specs that will run these games no problem.