I've had a similar problem for some time now. The starter would turn the engine over but it wouldn't fire.
Twice I left it until the next morning and it started without a problem. I too thought it was the battery so I fitted a new one but it has happened once more since. I also changed the ignition switch as I thought it may be failing intermittently at the same time. The leads, dizzy cap and rotor were changed about a year ago.
Only thing left were the plugs but as they had only done about 8K I assumed they were OK. I usually reckon to change the plugs about 12K.
I've since fitted new plugs and I couldn't believe the change it made in the driveability of the old girl. Much smoother.
The starting problem hasn't happened since, I'm hoping it's sorted.
So in this long winded way I'm saying dont necessarily rely on the plugs being OK. Good luck
