My car won't start, battery charger says its fully charged, yet the headlights dont go on but the radio and the inside lights are working.

Sounds as though the battery is no good,
unless you know otherwise & also had it tested
Charging a battery doesn't address it's internal
condition
You have battery cables that corrode inside & can be
voltage drop tested
You have the starter & solenoid,ignition sw & such, to name
a few,lots of possible causes & things to check

Sounds like the cable connections at the battery are not clean and tight, or a problem with power to the starter post, or the negative connection. The cig lighter is on a circuit of its own. Most everything else goes thru the key switch. The headlights are on a direct circuit too. But everything has to go thru the main battery cables.

have battery tested if good fully charge,then check all relays and fuses.

First make sure your battery is fully charged, you can atleast try and jump start it. After that check all fuses.

check and clean the battery posts first. Do the headlights work ok, and dim when you turn key to start?
Any clicking?

Try staarting in neutral. turn key to on, apply brake, shift to neutral, try to start.

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Does the horn honk? Headlight come on? Emergency flashers? If these things work it's time to check fuses. If they dont work you have a failure in the electrical system. Check the main fuse block under the hood or a shop needs to be visited.

#1 lights inside car mean squat they are very low draw how about radio heater headlights...and trying your ignition...I suggest you clean your battery teminal after fully charging your battery and make sure the terminals are nice and tight and then try starting your car w/out turning anything else on if it starts you have solved it if you drive it and it dies then you are just using juice in battery have alternator and battery lode tested at a reputable garage most will do for free on hopes of selling you what you need if they are ok then cherck your starter good luck

Dont know about security mode on the car, check your manual.
Check your battery by turning on your headlights and see if they work, if they do and work good then the battery is charged. If thats the case then it could be a security mode thing, if not a security mode thing then it could be a bad connection to the starter or a bad starter or starter relay.
Try the headlights first and see if you have juice.
If you donts check to see if you left a interior light on or your headlights, if so, recharge your battery and you should be good to go.
Good luck

the 12 amp is for a jump start and the 2 amp is for a trickle charge which doesn't degrade the battery. i believe you have a loose connection either a loose ground cable or the positive cable to the starter check these and tighten if neccessary

Is your charger working? Try jump starting it.