I am doing a motherboard cleanup right now for my Apple Lisa. Using white vinegar - which works well (50% vinegar/50% water), use a very soft toothbrush - and as Gibsaw says, clean *with* the traces. Clean off with circuit cleaner. After it drys, I will be testing with a low power meter to see that the traces are intact. So far, so good. I'll use a wire or solder to fix any trace issues.
Take care, don't rush - and test before firing it up.
Gibsaw wrote:mm.. yeah, If you use baking soda, make sure to dissolve it properly. Last thing you need is more contaminant and it can leave a residue.
Also, most ordinary unscented soaps are alkali. (Normal soap... not a "PH balanced moisture bar lovingly made by virgins by moonlight in a rainforest on the summer solstice")
An ordinary soap and water solution with cotton buds is an option...or like Tezza says... a soft brush if it's stubborn, but be gentle. clean with the traces. Loosen it and then dab /wipe it off with a paper towel.
If the traces survive, then circuit cleaner or isopropyl to finish the job, and I'll be "captain obvious" and say it has to be 100% dry before you turn it on.