What part of the ac system likely needs repair (please don't say whole unit) if the air will blow through the registers,but not very cool; set temp 73,hours later actual temp is 83; checked batteries on thermostat,outside unit not working,breakers ok,don't know what else to check; widow living alone,do not want to get taken by the repairman for a whole ac unit if it is just one component.

outside unit not working,breakers ok

You might check if the outside disconnect has fuses in it. Some do and some do not. Also sometimes the outside disconnect had a circuit breaker that also needs to be reset.

To reset a breaker properly you need to turn the breaker completely off and then back on. many people just flip the breaker back to on and that many times just does not work.

There are really no more used serviceable items for you to check but make sure you have checked.

The thermostat to be sure it is really on cooling and the temp set low enough to kick the outside unit on.

The air filter should also be clean. This will not stop the unit from running but it will have disastrous effects on the system operation.

If you cannot find the problem you will need a on site inspection and repair. Good luck.