There are a few candidates for what's behind your problems.
I think the group still needs more clarifying info.

You say there's no spark. What did you do to check for
spark? As needed, see
http://www.tegger.com/hondafaq/startproblems.html#checkspark
for how to check for spark. Note the caution (in red at the
site above!) about grounding the plugs properly so the coil
is not destroyed while checking for spark

Hot weather starting problems often indicate the main relay
is the problem. See
http://www.tegger.com/hondafaq/startproblems.html#mainrelay
. Has your main relay ever been replaced or re-soldered?

At this point, your engine may be flooded, and this is
behind it's not starting. To correct, see
http://www.tegger.com/hondafaq/startproblems.html#flooded

Did you use genuine Honda parts (= OEM parts) for the cap,
rotor, plugs, and coil?

If you hear the mechanical parts of the engine turning (and
it sounds like you do), then the starter is working.

How old are the car's ignition wires?  Tips for checking
their condition appear at
http://www.tegger.com/hondafaq/startproblems.html#leakywires
. If they're very old, they may very well be behind the
problems here. Again, use only genuine Honda parts for all
ignition parts. You'll pay more, but you get more life from
them and better car performance. I am frugal and learned
this the hard way.

These items are all very common causes of start problems on
a Honda Civic of your car's age. It's more likely it's one
of these (or a combination) than anything else.