Lenovo Cuts Out

I have two Lenovo 97027MG ThinkCenter A57. One of these has started cutting out randomly and unexpectedly. It then seems to try to restart; the fans blow for about a second, there is an audible click then it tries again. This is repeated sometimes for hours without success. Sometimes it eventually restarts and at other times will restart after a period of being disconnected from power. While it is ‘trying’ to restart the power button has no effect.

Anyone have any ideas? Thanks for reading this.