ASUS laptop won't start and I'm going nuts.

We have an ASUS laptop. It is 2 years old. We like it. It is a X530FN. Recently it failed to restart. This seems to be a common problem but ours is stubborn. At first we got by using the 40 second reset. Now it requires that the back be taken off, the battery and power cable disconnected, the 40 second reset done then battery and power cord reattached. It will start then. This can be a pain!
It will not start on battery alone. Will not start on power alone.When plugged in and refusing to start the battery charge light is lit. The "running" light is not on. After reset they are both on and we can start. This is the #4 problem listed on MyAsus so there must be an answer. Can't get any answer out of Asus though.

Here is what we tried.
Took it to an IT shop who replaced the motherboard.
Updated the Bios.
Made sure that all drivers were current.
Did all of the checks provided in MY ASUS
Tech checked our power connector and pronounced it good. Siad the battery must be OK since it was only 2 years old.