I have exactly the same problem with my Esprimo V5545. I went to shop to replace it, still the same problem. I don't know how to solve it, but I have figured out how to avoid it. If you pull out external power plug and then plug it in again, the notebook won't start. But if you start notebook on batery first, and when it starts loading plug in external power, then everything is Ok.
So, don't pull out the plug if don't need to, but if you need, then start on batery first.