Alright, I got my laptop back today. Here's what the sheet said they fixed:
System Board
Keyboard (I dislodged a ctrl key)
Switchboard PCA
Thermal Pad
The Thermal Pad is the closest thing to "fan" on the list. There's no checkmark ticking the "Heatsink Fan" bar on the sheet, so I'm assuming the fan was fine and the problem was the pad.
Which brings me here. Sorry, but can someone please explain what the four above-listed parts of the computer do? Thermal Pad especially. Could one or more of those parts be responsible for game lag if defective?