Test for bad DC board?

So I bought an A1278 on eBay.

The seller said that the Geek Squad told him:

"All it needs is a new DC board and a new battery"

I've changed DC boards in MacBook Pros before (not this model) plus I know they're cheap. So I bought it.

The night it arrived I tested with a known good charger. The light on the charger blinked between no light and a very faint green light.

Indicative, I thought, of a bad DC board.

I replaced the battery with a fully charged battery and....Nothing.

When I did this with other models with bad DC boards they started up.

I see no evidence of water damage. It does look like it was pretty dirty inside, possibly enough to cause fan failure/overheating.

My question is:

Does this mean it's more likely the logic board or is it possible that it's still just the DC board?