Many people are complaining about this same thing. Apparently it is an LG DESIGN DEFECT where one of the charging pins on the main board breaks off. LG offers a 1 year warranty on the LG Rumor, but according to other people they are REFUSING to honor their warranty commitments. I suggest filing an FTC complaint against LG if this is the case for you. For more info:
LG Rumor not charging - warranty not honored | Geldpress