I don't even have a Factorio folder in that directory, probably because it's created on the first start-up of the game

How do I find a log file? I'm not even getting error messages at the moment.

From msinfo32

OS Name: Microsoft Windows 8.1
Version: 6.3.9600 Build 9600
Other OS Description: Not Available
OS Manufacturer: Microsoft Corporation
System Name: USER
System Manufacturer: Dell Inc.
System Model: Inspiron 5423
System Type: x64-based PC
System SKU: To be filled by O.E.M.
Processor ...

I bought the game today from Steam and installed it. I tried to run it, both from the steam client and from the factorio directory (as an admin), and nothing comes up at all. Factorio appears in task manager as a background process for less than a second before it disappears without any error ...