Okay, that mower was never registered by the first owner, so the warranty clock starting date is when the mower was invoiced to the dealer from Honda, 3/3/2012. With a 3-year warranty, it will expire on 3/2/2015, so plenty of time left. That serial number also tells me your mower
is in the affected range of mowers that may have a sticking autochoke. Note if you are the original owner, and have paperwork showing the date of purchase to be after 3/2/2012, a Honda dealer can update the records in the Honda system and reset your warranty to the date on the paperwork + 3 years.
The first thing to do is to determine if the no-start is actually caused by the a sticking autochoke. Your Honda dealer can do this, but if it is determined
not to be sticking autochoke, nor any kind of factory defect, any repairs you authorized will be out of your pocket. Please note some dealers might charge a diagnostic fee to troubleshoot this kind of problem, others will not. All Honda dealers will cancel any diagnostic fee for repairs covered under warranty. Be sure to discuss the options with your dealer and tell them not to do any billable work without your prior authorization. Be aware this is a very busy time of the year for most mower dealers, so it make take a few days before they can make progress.
You can locate the nearest Honda dealer at this link; be sure to check on SERVICE and LAWN MOWERS then type in your ZIP code:
Find A Honda Dealer
It is best to get this problem resolved by a dealer, especially as it sounds like it may be covered under warranty. I don't recommend DIY for this job, as it is kind of involved to remove the air cleaner, carburetor, all the guides, gaskets, springs and linkage rods, then extract the thermowax cylinder from the engine block, etc. Not for the faint of heart. :confused2: