MacBook doesn't charge anymore. Logic board error?

So my old Blackbook started randomly shutting down the other day, and having had a (swollen) original battery in it for the last two months, it made sense when I realized the battery wasn't charging anymore.

Hoping it was just that, I got a new battery, but that wasn't charging either. Having reset the PRAM several times, I tried applying the SMC updates available (I run 10.5.8 and the system told me they were unnecessary), I finally got a new Magsafe board and installed it. Didn't help either.

The macbook doesn't charge and won't run on the adapter. The LEDs on the Magsafe connector turn on, but go green, no matter what the charge on the battery is.

I have tried it with both the new and the old battery, and with two different original Apple power supplies. The laptop will turn on as long as there is a charge on the battery.

Do I have a more serious issue on my hands? Bad SMC?

The macbook is from 2007. Model A1181. Core2duo 2.16Ghz. Last three of the serial are YA9.

Hope somebody can help. Thank you!