Laptop Not Getting ON after Long Switch OFF

Hello,
i have a thinkpad which was working for so long without any problems.
Now it is not getting ON when it is kept OFF for more than two days.
when pushing the ON button and connecting the external charger simultaneously ,it will switch ON properly and works with no problems.if it is swiched ON for say 3 to hours,it will switch OFF and ON without any problems and works normally if it is used everyday.
When it is kept OFF for more than 2 days it wont switch ON normally and only i can see the green power LED.
It seems the laptop is not getting the 5 volts from its motherboard as i cannot even operate the DVD drive.
Do you think that it is something to do with a capacitor on the motherboard,because it works normal when it is used daily.

Thanking you in Advance for your help

Abraham