It should auto-focus and stay there like your old computer did, there's no way to change this behaviour via a simple setting.
So it sounds to me like you have something wrong with your new computer.
Try it in Safe Mode, if it works as expected, it's a piece of 3rd party software that's running and interfering. If that's the case then you can use MSConfig to disable things, and then re-enable them one at a time until you identify the culprit.