That usually indicates that you don't have any military funding or you don't have a starport built.  You need at least 1% military funding (or Focus on military on a planet) to build ships.

Open your ledger (F4) and drag the sliders for military, social and research around (note that their position does not always reflect the actual percentage, they're wonky that way).

Once you get a starport up, and start a given ship, yo can play with the sliders in your economic screen and then see what it does to your completion times for that ship.  I found it gave a real good feel for how you were affecting military production.  My understanding is that it also depends on manufacturing boosts such as factories and asteroid mines.  Not too sure about how much population affects affects ship manufacture, but it seems to for me.  Others will probably have more accurate formulas for the whole thing.

Also, your total spending slider is a factor.

That is, a planet's military production (excluding asteroid stuff) is a multiplication of (your total spending), (percentage applied to military), and (the sum of your on-planet facilities).  Thus, you could be spending very little and have the percentage slider 100% the way to military and get little or no military production.

Also a factor is the state of planet habitability.  If you cannot colonize the planet (say you capture/trade for a toxic planet though you cannot colonize it), then the factor will be zero.  If you have half the colonizing tech, then 0.5.  If the type is your native type or yo have fully researched it, then it is 1.0.

From the two explanations, I am hearing that population may indirectly affect military production.

More population = More taxes = More spending = More Military spending from slider

All that is then combined with the calculations for on planet buildings and asteroids, which do not depend on population.

Is that correct?  I ask because I see military production inching up in increments smaller than I can account for otherwise.

The debt ceiling is 500bc, if you're at -500bc or lower, all production ceases except some focus production!

As stated before, population has no direct bearing on production, it only determines your income but doesn't determine your military expenses as taxes are not tied to expenses (it does factor in at your maximum espionage budget though). You can run all your factories at full production regardless of whether you have the taxes too offset the deficit, it's just that as soon as you hit that debtceiling, the plug is pulled...

You are charged fully for asteroid production. Bonus production from moons and starbases works like all other bonus production: you are charged only for 50%.