This...MIGHT...work...
1.) Start up Team Fortress 2.
2.) Go to your options.
3.) Set your game to windowed mode. (It's in options...you can find it :3)
4.) Close your game.
5.) In your steam games list, right click on Team Fortress 2.
6.) Click on properties.
7.) Click on SET LAUNCH OPTIONS...
8.) Type in this exactly without the quotations, "-noborder"
9.) Launch back up Team Fortress 2 and see if it works.
Now if anything happens, just alt+tab (It doesn't downsize the whole game window, it's something like Windowed Full screen in World of Warcraft/WoW), and then go to your task manager by hitting CTRL+ALT+DEL, then clicking on Task Manager, if you're on windows 7 right click on the bottom home bar, and then click on task manager.
Lastly click on Performance while you're in an eGO server (Get into the eGO server before doing all of this, but you should have known to do that anyways.), and then reply with your CPU Usage, and your Memory that's being used. (It'll have a number right below the word such as "CPU Usage", or "Memory".)