Blue stuff on the battery terminals is normal battery corrosion. All you need is a toothbrush, water, and baking soda to offset the acidity.
How to Clean Car Battery Terminals | Cleaning Guides
Check to see if the battery terminals are on tight. IIRC, factory Honda battery post are sometimes a tad smaller than the clamps. So if they are not properly tightened, you may not have a good connection between the car and battery.