I don't know what the issue is with my 1999 Neon. But when you turn the AC or Heater on the belt and ulleys all cease up. Can anyone tell me what the issue is so I can fix it

 

The problem is with your AC compressor. More specifically, the AC clutch. When the AC is on, or the defroster mode is on, the AC kicks on to remove excess moisture from the air.

If the AC clutch is bad - and it sounds like it is - then this occurs.