Going by the serial number you gave, and your description of how the controls move, I believe this is the owner's manual to your mower.
http://powerequipment.honda.com/pdf/manuals/31VE2630.pdf
Take a look at it and see if the controls look like the ones shown in the manual. If you have the numbers 1 and 2 on the control panel next to the orange lever, then you have a gear driven mower.
There are no switches, such as electrical switches, involved in either the blades or the transmission. Just a cable that is attached to the levers at the handle bar end, and a pivoting arm at the other.
After you have pushed down on that yellow button, and move the lever it is on forward toward the handle bar, you should feel tension, or resistance in that lever. You should feel that tension begin after you have moved the lever forward about a half an inch, or so. You would definitely hear the blades begin to spin, and see air blowing from under the deck if they are being activated. When you let go of the lever, it should spring back to the off position on it's own.
Here is a test that I always do on mowers like yours when I come across them to quickly see if the transmission and it's belt are likely O.K.
With the engine off, push the mower forward. You should hear a clicking sound coming from the back wheels. Then, again, with the engine off, push the drive lever forward, and try to pull the mower backwards. The back wheels should lock and drag on the ground and not roll.
Take a look at the owner's manual. It contains most of the information you'll need for that mower, and try those tests I mentioned and see what results you get.