I have an old A/C, Rheem RENB 1005. The AC is running since 8 am, and at 6 pm, the temperature is still 85 degrees in the condo. I am located in Miami, on the top floor, 5th floor. The blown air is cold, but not cold enough. What could be the problem?

Ruud AC 14AJM49A01 was installed 4 years ago (2014). We were away for a 3-week vacation on May 2nd and set the thermostat at 88 since nobody would be home. Returned home on May 24th with temperature at 85 in the house, set the thermostat temperature lower to 79, and heard the fan in the house running and realized after a few hours it was not blowing out cold air. Checked the filter and found it was completely blocked. After replacing the filter, fan in the house still not blowing cold air. Went out to check the unit, found out the fan is not running and little humming sound coming from the unit, presumably from the compressor. Gave the fan a little push, but fan is not turning at all. Shut off the AC and turned on again after a few minutes. As soon as it turns on, a loud sound came from the unit (compressor?) with the fan not turning, after a minute the sound stops and become a little humming noise with the fan still not turning. Thinking of replacing the capacitor. After opening the cover found out there is only one capacitor with two terminals on it and it could very well be the run capacitor for the compressor with ratings 45mfd/370V (43-101666-37)and didn't see any other start capacitor nearby. The question is why is there NO start capacitor for the outside fan? Is it possible to have the no such start capacitor? How would the outside fan motor run without capacitor? There might have been a few days during the 3-week vacation period with high temperature that caused the AC to turn on the whole time with the outside fan already not running. Still waiting for the run capacitor 45mfd/370V I ordered. Any helpful suggestions would be greatly appreciated.