It could very well be the Magsafe board that is not charging:
[product|IF186-019]
http://shop.ebay.com/i.html?_kw=A1181%20magsafe&_clu=2&_fcid=154&_localstpos=&_stpos=&gbr=1
or as in my case I changed the battery cable which contains some electronic that could be damaged by liquid. This cable tells the logic board if the battery needs charge, is present at all etc. Here it is:
[product|IF186-015]
Just remember to get the correct version for your MB.