I have a hs29-024-1P. The compressor starts but the fan motor does not. If I give it a little push it will get going. Does this sound like a cap problem? Which cap?

Yes ,probably. If it has 2 caps it will be the smaller one,the one with the lowest number like 5 or 7.5

Thank you. My unit has a start capacitor and a dual run capacior. Do you think my problem is in the start or run cap?

Well not being there its just a guess, does the start cap go the fan motor or to the compressor? Or both? Since it won`t start on its own,and the start cap is attached to the fan motor a good guess would be start there... they are a lot cheaper than buying a motor.. is the top of either swollen upward any at all? They should be flat,, this would be a good sign if you don`t have the testers to check them out right