There is probably about $3 - $4 worth of gold in a CPU. There would be more in a motherboard.
The best way to recover gold from electronics is to use a combination of concentrated nitric acid and concentrated hydrochloric acid; a volume ratio of about 1:3. That combination is known as "Aqua regia". It is pretty corrosive and dangerous and best used in a well ventilated room since using aqua reqia on electronics (or just about anything) results in toxic fumes.
To give you an idea about the amount of gold, my brother in law does this. He's been doing it for around 2 or 3 years. I have no clue how many parts he's recovered, but its a lot. MANY computers worth. So far he's up to just over 1.5oz. I believe he has told me before that one whole computer is worth around a couple of grams.