My headlights wont turn on everything is good 1996 hyundai accent

Most likely the headlight switch itself. Most head lights do not have fuses

Check the bulbs could be blown low beam

Hi I'm Peter, check the fuse box under the hood there is a fuel fuse and a fuel relay then check them. Use a meter to check the fused also check at you are getting voltage to the fuse by using a meter touching each of the post where the fuse plugs in when the key is on you should have power to one of them but not the other with the fuse out. There are several relays that are the same part number as the fuel relay so you can check it by just using one of the relays like for the horn or headlights. If all that checks out look for a port on the fuel rail to put a fuel pressure gauge on and see if the is any fuel pressure. Could be a fuel pump if all the other things I mentioned are in good working order. Let me know what you find . Good Luck

No, I wouldn't suspect the headlight switch. Something more sinister, more surreal, too: a module, maybe a body control module, or a light control module, probably under the dash somewhere. GM began using a lighting control module (LCM) at least as far back as 1992, tucked unhandily up under the dash, and wired between the headlight switch and everything else in the lighting circuits.
Normal to suspect the headlight switch, but the odd conjunction of the car running and the headlights' actions suggest a module (another computer!) may be in there. The headlight switch should have no effect on it if the engine was running or not. You would have to see a wiring diagram in a repair manual to check. I am not familiar with your Hyundai, but if you could find a diagram, you should be able to fix it.
If you register for free at autozone.com, giving make, model, year and engine size of vehicle, you can access wiring diagrams and repair procedures. Just look under repair guides.
Wiring diagrams were under Chassis Electrical, if I recall.

Get a schematic and trace out the power source to those devices not working.

Could be Headlight relay, bad ground, bulbs blown, fuse blown or unplugged connector under the hood. The interior headlight switch is a long shot. Make sure everything under the hood is hooked up. Look around the firewall or headlights for unplugged connectors.

headlight switch or high beam switch if you have one

Under the dash fuse box ,fuse 15 (TCM ECT) is a combination of cluster, heater and headlights.probably a relay fuse!!!!! fuse 16is a relay fuse.

It sounds to me like you might have a loose headlight connector, or something is causing the conduit inside the headlight to shatter, if you take the car to work every day do you go over a big bump at all? also what brand are you using and what does Hyundai recommend using, the wrong headlight bulb can also make this happen - just because it fits doesn't mean its right.

Lihgting switch must also be checked