Yes, a spoilt motherboard can be repaired but the cost of doing so must be compared with the price of replacing the computer. Although your data will be safe during the process of such a change, since no data is stored on a motherboard, pretty well everything has to be replaced so it isn't an easy or quick job to do yourself, and it is expensive to have it done for you. The only exception is if it is under guarantee, or if it is insured. Then go for it but back up your data before parting wth your pc to a repairer.
When it comes to repairing a bad motherboard, several things have to be taken into account. The first thing is to be able to locate any of the damaged capacitors. If you are able to do that then that could be a solution. If there are any obvious faulty components that are on the motherboard then they too have to be examined and most likely replaced. There are also checks that need to be made on the motherboard such as the power supply unit and completing the power on self test. Problems with the video card or graphics card could also make a person to look to the motherboard for any problems. Static electricity can also do damage to a motherboard. The certain answer is that yes a motherboard can certainly be repaired. It will take some diagnosing to see what components may be malfunctioning but yes a motherboard can be repaired as long as there are no bad cracks or any other things that may be comprising the structure and functioning of the motherboard.