Sounds like you need a bigger iron or a bigger tip for your current iron. If the connection you're trying to solder is part of the ground plane of the motherboard, or just very large, it's going to take a lot of heat out of your iron's tip right away.
Two thoughts come to mind:
1) You could look for somebody in your local area that does electrical repair and see if they could perform the soldering for you. Any TV shops still in business? They might have the finesse necessary not to damage the board in the process.
2) Contact customer service, explain the situation, and ask if they will repair the board (for a fee of course, as this isn't a warranty issue.)