When I turn off the ignition key the radio and dashlights stay on until it runs down the battery

If you turn car off and remove key from ignition, th? headlights will stay on until you open the driver side door, its part of an auto on headlight system. you can leave your selector light switch on the headlight position or on the daylight lamp relay (DRL) position. and open the driver side door and the lights will go out and not stay on. so it saves running your battery down. That feature is only on SLE trim line on the Solara.

It could be your key is bent or the ignition switch is not turned all the way off to the right. Having too much keys on the keychain can cause this problem. Turning on the alarm will assist you in case you leave the car and the radio is still on. The alarm will go on, that way you don't come out to a dead car battery. Hope it works out for you

This sounds like an ignition switch problem.
The accessory is staying on after it should be off.

Did you do some electrical work on the car?

The 2000 Fords should allow the radio to continue to play until you open the driver's door. The lights may stay on for 1 or 2 minutes after you leave the car (close the driver's door) depending on the lighting/security feature of your vehicle.

Your battery should be strong enough to allow these items to remain on for several minutes. If the battery weakens that quickly, you need a new battery or you need to have your charging system inspected.

Sounds like a battery cable problem. Check the battery cable terminals for corrosion and tightness. If those are fine, have a load test done on the battery.
Here is some troubleshooting tips:

Battery terminal connections loose of corroded. Check the cable terminals at the battery; tighten cable clamp and/or clean off corrosion as necessary.
Battery discharged or faulty. It the cable ends are clean and tight on the battery posts, turn the key to the On position and switch on the headlights or windshield wipers. If they won't run, the battery is discharge.
Automatic transmission not engaged In park (PI or Neutral (N).
Broken, loose or disconnected wires In the staging circuit. Inspect all wires and connectors at the battery, starter solenoid and ignition switch (on steering column).
Starter motor pinion jammed in flywheel ring gear. II manual transmission, place transmission In gear and rack the vehicle to manually turn the engine. Remove starter and Inspect pinion and flywheel.
Starter solenoid faulty.
Starter motor faulty.
Ignition switch tautly.
Engine seized. Try lo turn to crankshaft with a large socket and breaker bar on the pulley bolt.
credit: https://www.wc-autoparts.com/blog/trouble-shooting-no-start-condition-19932002-camaro-and-firebird/

buy a new battery if this dosnt work trying looking into a starter or ignition relay or coil pack this all will make it not turn over but the radio and clock will work, also look into if your security light is on if so the key could be broke which would make it a problem cause then you have to go to a dealership and buy a new one which might cost a bit. hope this helped :)

wow.....ok sounds like your ignition switch is starting to go bad .......the clue is both dash and radio if there was just one staying on i would think otherwise.....good luck

HAVE CAR SCANNED SOUND LIKE CAR IS IN THEFT DETERENT MODE.IT HAS DISABLE YOUR IGNITION SO CAR WONT CRANK.LET DEALERSHIP FIX IT.

You Should FIRST Rule out the Ignition Switch this can be tested with a test light-by, Probing the "ACC" Terminal @ Fuse Box with KEY OFF, If there is Power at this or Any KEY ON Power Source when the KEY IS OFF, you Have a Faulty Ignition Switch. IF NOT, then the Test Light can be Used to Locate the CIRCUIT Where the Battery "DRAW" is in, Do this By First Disconnect the Positive Battery terminal,Connect the GROUND end of Test Light to the + pos Battery terminal and The "PROBE" End to the + Pos Battery "CABLE" With KEY OFF and All Other Electrical OFF the Light Should NOT Light up, If it Does Light Up, Go to Fuse Box and One at a Time Remove and Reinstall FUSES Until TEST LIGHT Goes OFF when you get to the FUSE that TURNS OFF the Test Light THIS is Where the BATTERY DRAW IS, you must then Locate the Faulty Component and Repair/ Replace the Part.
I truely Hope this is of Good HELP to you, And if You Have ANY Questions Feel FREE to Reply I Will Be Happy to Help ! Have a Good DAY !