From what you are saying this sounds to me like a background process such as an antivirus sweep or check, or possibly an update service running out of schedule, that is taking up enough system resources that it's impacting your ability to play games. Those are much more resource-intensive than simply browsing and you would be much more likely to notice the type of lag you are suggesting.
Start a ping trace with a command window. Ping -t 8.8.8.8 will ping Google's servers endlessly until you stop it with ctrl-c. Play TF2 or whatever. Wait for lag spike. When it hits, tab over to the command window. If your response time (ms) is significantly longer (like from 17-32 to above the 100s), it is likely network related. If it is not, then it is hardware or software related. Alternately if it takes forever to tab over you may be looking at an in-house problem.
Does the entire screen freeze and go real choppy with a super low framerate or are refresh rates (such as leaves blowing in the wind, characters breathing, waves and clouds etc) still occurring on screen? Again this will help diagnose the cause of hard/software vs. network, latter suggesting network.
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