Hi,
It seems like a problem with the AC adapter since it's not powering the laptop without the battery connected but here are some more troubleshooting steps to help in identifying the issue.
- Do a hard reboot first, remove the battery and unplug the AC adapter then press and hold the power button for 20 seconds then try booting it up again.
- Next to try is to remove the battery again and power it on with just the AC adapter connected. If it will still not boot up, do try a different AC adapter that has the same voltage with yours and see if it will power the laptop or not.
- If using a different AC adapter will also not work proceed with reseating the RAM's, remove them all for couple of seconds then put them back in and see if the laptop will boot up or not.
- If all these will not work the problem is the motherboard already.
- Do contact ASUS for a repair if the laptop is still under the factory warranty.