Hello, have replaced contrl brd, start compacitor, I get 4 flashes which means limit switch, bypassed all limit switches.

I've got an old Carrier condensor that's been acting up the last few days. Sometimes it'll blow cold air and sometimes it won't. I went outside to look at the condensor when it wasn't blowing cold air and noticed the fan wasn't turning and I could hear a loud humming. I tried the start test by using a long screwdriver to push the fan blade but I couldn't really get it to start - maybe I didn't have enough leverage. One thing I did notice though is that if I turned off the AC from the inside, then I could make the fan blade spin just fine. My initial conclusion is that the issue is the run capacitor (also called fan motor start capacitor I think) so the fan doesn't have enough power to start - and if I had more leverage, I could probably get the fan to start by pushing it. The strange thing is that if I leave the unit off for many hours and then start it up again, then the fan will turn iand t will cool the house down fine. Also, I'm not sure but I think it seems to work fine when it's cooler outside - because so far, it's been working fine though the night but usually doesn't work much if at all during the day. Could any of the experts here comment? Am I on the right track with thinking I should replace the run cap and if that doesn't do it, then replace the fan motor? Can anyone explain why it seems to be working sometimes? Thanks in advance!