I have an Acer Aspire 5672, it just cut out &

One thing you might try is to unplug it from the adapter and remove the battery. Let it sit a few minutes and replace the battery and try to start it again.
If that doesn't work, then plug it in and try it again.
If it still won't power up, you are probably looking at a motherboard that has gone bad. If it is still in warranty, then the company should fix it.