My 2004 dodge neon will not start head lights and radio work no dash lights.

Sounds like the Security Light

https://dashboardsymbols.com/2019/06/warning-lights-and-symbols-seen-in-dodge-vehicles/

https://www.google.com/search?q=2004+dodge+neon+dashboard+warning+lights

..

Fuse

Try pressing down on the red security light on the dash and hold it down for about 3-5 seconds. Sometimes Neon's just have a dummy light on the dash that isn't actually hooked up to anything, but its a good place to start.

you might have a short on th eback of your fuse box.. if not tthen I would start by disconnecting the power wire to the radio. (as near the fuse box as possible maybe even the ground wire too (although it will still ground through the antenna). if the radio will work independently of the fuse box (still with a fuse in the line always fuse any electrical device in the wire route) then you know the radio isn't the problem and thus it is a wire that deals with the radio via the car. .you have to be careful that you don't damage the computer while blowing fuses. if it's the radio then off to the pick a part junk yard..

Sounds to me like a loose wiring connection behind the dash or possibly loose fuse connections

Hmm....Dodge Neon 2002....okay problem is with wiring maybe.....

try replacing the battery.

How old is the battery? Clean the connections, charge the battery. Try starting it. Get the battery tested at Autozone or some place like that.

You might want to check for a loose ground (negative) wire somewhere. That could explain the popping with the radio.

Try giving it a good rap on dash above speedo, see what happens, and get back to me, it may have same problem as my old 95' neon did.