I have the same issue, MagSafe light is DIM Green (barely noticeable). Been troubleshooting with Apple Support. So far replaced battery and charger. Tried Original 60w and New 85 watt known working chargers. I have also reset the PRAM and SMC and still no luck.
However, it now powers on (can hear fan(s), CD Drive and power is indicated via the power light on the front panel). However, the MacBook Pro still will not charge the battery, no display and no caps lock light.
I have taken it to a local Apple Store yesterday, they kept it overnight to look at it so I should hear from them today. They will try to confirm the issue or fix it with some resets I am told. However, I asked what is worst case scenario since this is a Mid 2010 MacBook Pro as I don't want to spend $500+ on a logic board and labor. The guy stated that they have a flat rate repair for this for $280 (less than $300) that will include all needed parts and labor to fix this. I should have info later today and will pass along either the fix or if it will be sent in for the $280.
Considering the machine is in still like new condition I would be willing to spend $280 on it. I have other machines but this is a work horse for what I use it for.