Honda Repair: starting, honda accord lxi, transmission failure

Question
my 1987 Honda  Accord LXI has been starting with no problem, until a couple days ago.

When I turn the key over to start, the starter spins the flywheel, but the engine won't start.

 I have checked to make sure that I am getting fuel to the engine, and I am.
 I have checked to make sure that I have spark from my coil to my spark plugs and I do.  
 I have checked to make sure that I have spark from my spark plugs to my engine and I do.  

 I don't know what else to check.

I just flushed out my radiator last week and everything there is fine. Also we put in another
automatic transmission last week because mine had lost its gears.

ALso my honda had sat not driven for 4 years due to the transmission failure.  I went out and started it every now and then and had no problem starting it then either.

ANy suggestions?

Answer
Glenda:
There are two elements and you have checked them both, fuel and spark. The only thing I could suggest is that one of the components, in the ignition is not delivering enough spark to fire the engine (starter or battery).
Sorry I can't be of more help.
Bill