|If under warranty or warranty for the repair, send it back.|
If you can get it up and running, install HWMonitor and see where your temperatures are, if they are high on a start up and climb steadily, you may have to send it back since either the fan is not running or the heat sink was not installed correctly (there cannot be dust build up if they just rebuilt it).
When he said to turn off the auto restart it is so that you will get the error message so you can post them or Google them for additional clues to follow up on. You getting 15 minutes does sound like a heating issue so it is worth looking into also.
It should be obvious, but make sure that the 'laptop' (should be called 'portable computer') is flat on a hard surface to allow proper air flow through all of the vents. Most laptops are not really suitable for gaming so back down on all settings in order to play most of them and learn how long you can play before heat becomes an issue, especially in summer.
You have to be a little bit crazy to keep you from going insane.