Soldering capacitors on a modern motherboard is
very tricky. They have many 'layers' and the components are crowded very closely together -- not designed to be repaired. Are you a professional technician? Do you have access to professional equipment? If not, the odds are quite good that you'll just further ruin the board. (I would say "Even if you are, it's not likely you can fix it." but then you would know that...
)
Unless this board is some sort of 'collector's item' you're much better off just replacing it. You might be able to find the same model on eBay or on one of those 'discount parts' sites like Pricewatch.com if you search a bit.