What do you hear when you turn the key in the ignition? Just
clicking? Or does it sound like the engine is actually
starting to move?

If just clicking, check the battery voltage first.

How old is your Civic? How many miles? What is its
maintenance history?

My guess is the battery connections gave up. A voltmeter, if you have one,
is the very best way to check. You can do a crude check for bad connections
at the cables by pushing a penny or pocketknife blade down hard along the
joint between the cable end and the battery post, then twisting a bit. If
you see sparks you've found the culprit.

Batteries sometimes fail from internal conductor cracks. A voltmeter is
pretty much required to check that out; if the voltage at the battery posts
themselves is way below 12 volts with the headlights on the battery is bad.
I am not suspecting the alternator because you reported the headlights being
on and working until you tried to crank the engine, then they quit.

If the problem isn't at the battery you need advice from somebody here who
has experience with the battery fuse.

Mike

Dead Battery, been there done that.

G-Man