Try removing the battery and wall power, hold in the power button for about 30 seconds, plug in wall power only and see if it turns on. Try different RAM or one RAM stick at a time. If that does not help, open the system, remove the CMOS battery along with the other power, hold in the power button for 30 seconds, then without the CMOS battery or normal battery plug in the charger and see if that works. If it does, replace the other batteries and see if it works now.
If not, replace the charger and see if that helps. If that does not, issue is likely a dead motherboard.