1. Wire the laptop to the router.
2. For each game research server disconnect questions and answers.
3. What's not stock on the machine? Anyone add Mcafee, Norton or other "protection suites?" Why I ask is for gaming these can often step in and block. Avg/avast offers a game mode due to this issue.
4. Laptop gaming can cause the machine to heat up and see WiFi and other problems. Get wired as in step one and place the laptop on a cooling pad.
I bought a used Lenvovo ThinkPad. My son plays online video games and I knew it would run them better than what he had. In the middle of playing online games he will get disconnected from the server. This happens across multiple games. When this happens the laptop also won't connect to certain websites like forums. I think this is because it won't connect to the sites "server". Would really appreciate any help.

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic