Air Con units already have starting Cap's, as a matter of course, for both the fan and the compressor.
Most compressors are split-phase anyway, as far as single phase ones go.
3 phase compressors are self-starting.
You wouldn't by any chance have a loose Main Neutral by any chance?, I've seen this happen before!.
[Message edited to add further comment]
[This message has been edited by Trumpy (edited 10-04-2003).]