Headlights won't come on at start, please help!

When i turn on the engine, and then turn on the headlights, it would take like 5 minutes later for it to turn on, i don't know what's wrong with it. Perphaps it has to do with the engine being so cold because it is winter right now. Before there was snow, it turned on when i want it to. I think my civic has wiring and electrical problems because a few months ago the whole interior dashlight/rear tail lights were all dead. I had just replaced my batteries, i think they're the right one.

dude can write alittle more clearly? are you trying to say your it takes 5 min for your headlights to come on or your engine?

it takes 5 minutes for my headlights to come on after i turn the light switch.

BTW u have a 93 civic DX for sale?? i need a bolt for my civic. It's the one that holds the license plate to the trunk. The picture shows where the bolt is.

http://mi.aacdn.us/RBBoyz/vcbvc.jpg