First you should determine if the system will work off the battery. Install a '''fully charged '''battery from another D610 and see if it will boot. If so, then let windows load completely to the desktop and plug in the charger. The power indicator in the lower right should indicate ''on AC'' if the power adapter/charger is functioning. If you do not have a power indicater, you can look at the function by going to control panel and opening the Power Options icon and clicking the power meter tab to view if your system is working on AC power on not. If not then the adapter is suspect and should be replaced.
If the new adapter doesn't fix the problem your AC jack on the motherboard may need to be replaced and should be checked by someone that does quality repair work..
I hope that helps, Good luck