Only a couple of things left that we can check, do the easiest first.
Disconnect the LAN cable from the computer and test, it would be better if you had a game stored on the computer that you could play or a video that you could watch, this to put the GPU and PSU under load to see if the computer locks up, if it does, you have ruled out being connected to the internet/a LAN problem as the cause.
Let us know how this goes.
Disconnect the LAN cable from the computer and test, it would be better if you had a game stored on the computer that you could play or a video that you could watch, this to put the GPU and PSU under load to see if the computer locks up, if it does, you have ruled out being connected to the internet/a LAN problem as the cause.
Let us know how this goes.