I have 2004 dodge neon. It wont shift into high or reverse, whats the problem?

You are guessing and guessing is expensive. You need an auto-electrician with a pro grade scan tool computer. The electronics diagnostics with give the answer to what failed when you went into reverse. I'll give you a guess, it is something on the gearbox, or a computer network failure between it, the BCM and ECM.

This vehicle certainly has some issues.

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That mean you have problem with transmission.

Yes, it could be the transmission control module or a shift solenoid in the transmission is plugged up or burnt out so it doesn't shift up.
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Here is some info. about fuse locations on the 2004 Dodge Neon.

Circuit Protection Fuses Fuse block

Fuse block fuse location

Power Distribution Center (PDC)

PDC fuse and relay location

RUN it could be a bad tranny

Or have it checked by a pro tranny mechanic just in case it is only a sensor issue, i see a lot of neons with this problem.

ok i just replaced mine to but you have to make sure that you replace the throwout bearing(correctly)
if this does not happen it is like the clutch is engaged partially all the time and another thing is that make sure no oil is in the clutch pack. i replaced my main engine seal while i had it apart because it was tossing oil into the clutch area.

Good Luck

its a sudden transmission failure and needs to be taken to a shop it can be the gears binding or a clutch problem