1999 Dodge Neon bad A/C

Did you checked the relay on firewall where the wires go from the compresser up to a little connector on firewall. I had to replace that relay on a neon I use to have which had same problem you say you are having just track wire from compresser up to a small black connector on fire wall where the compresser wires go into and its also a relay swithch to find out if thats the problem unplug compresser from wird connector use a jumper wire and jump between the connect sides if a/c compresser works replace that connector. From any auto store or most liklly a NAPA store. Good luck.