This is probably one of the toughest parts in the game. You'll need a lot of luck and quick reflexes to make it through. Approach the door and wait for Vasquez to breach it. Follow him inside and work your way to the control room. Pull out a shotgun and move into the room with the computer towers. Clear it out and move forward to the main room with all the TVs.

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Alright, to survive we need to get to some cover. If you didn't follow my advice and grab a shotgun before, there's another shotgun right by the first cubicle. Grab it and move forward. Go into the office area directly across from you and clear it out. There should be about 2 men inside, but they might run out. Kill them and move toward the other room ahead. Look up and take out a guard who may be on the balcony. Then continue to fire and wait for a moment. You probably should just wait for Vasquez to make it up to us. This part is a lot easier if you have someone watching your back.
Your biggest problem is that the soldiers love to throw grenades at you and they'll also storm right in, so watch the door and wait for an ally or two to show up. When the coast is fairly clear, run forward to the other little office across from you. Kill the man inside and lay down. Watch the door and stand up carefully. Keep firing and thin out the crowd. There's a little hallway just to the left of our office. Go inside and use this area as a defensive position. This should stop the spawning. We just need to hold out and kill the stragglers. Once the last one dies, Vasquez should advance and open up the double doors.
Follow him out and join up with Griggs' squad. Follow them upstairs and out onto the roof. Watch the parking lot for the new group of enemy soldiers. Take some of them out while you wait. Griggs should open up the doors in back. Move in and go over to the next door in back. Stack up with the marines and wait for them to breach it. Storm the TV station broadcasting room to realize that no one's home.