It could also be a stuck Thermal Expansion Valve (TXV) that is preventing refrigerant flow and jamming the compressor.

The 35/5 should have done the trick if it was bad
Sometimes on real old compressors i put a booster on .
Fan runs or doesnt ??

Uh, oh. I assumed from your posts the fan was operating normally and the compressor wasn't. If the fan is still having problems this puts an entirely different light on the problem. I'd concentrate on the fan first. It's really simple, it's a permanent split capacitor motor.

Single Phase Motor Starting

The fan could not start without the capacitor, there would be only one winding energized. The fact that it will start but then stops, and then restarts sounds like either a capacitor problem or a connection problem. If you can get the fan to work, whatever you find will probably apply to the compressor also. I'd recommend disconnecting the compressor and working with the fan alone until you find out what's going on. Don't what to shell out the compressor with your troubleshooting efforts..

Okay Update time....

Initially the fan wouldn't spin and the compressor struggled.

I dug into it today and the Capacitor seems to have resolved/helped the Compressor problem. Coils are getting hot but airflow is low through the condenser.

The fan spins ok by hand. With the new capacitor the fan now starts slow but never gets full speed. Eventually it slows to a stop and the cycle begins again. When it stops the fan is hot hot hot. Compressor is cool (not hot or cold just cool).

I am beginning to think the Cap and the fan died at the same time. So you are correct to fix one problem and then the other. I am going to get a new fan this week and see if we are good to go. If not I will look harder at the compressor but hopefully it will be ok.

I am still going to get a whole new unit but I would rather shop ahead of the failure instead of in an emergency situation.

Thank you all for the help and advice.

I still wouldn't rule out a bad cap. Especially if the fan isn't coming up to speed.

If the fan is working at all, the motor is probably fine. The fact that it's cycling still points to a capacitor problem or a poor connection problem.

With the additional information
it points toward your 1/4 HP at 1075 RPM FASCO fan motor having developed a short in its winding
and opening its internal thermal protection switch as the electrical arc inside heats things up.

You might be able to smell the internal arc burning.

Pulling an old fan hub off an old motor shaft can inspire you to invent new curse words,
especially if you do not have the right puller and rust penetrant spray.

Sometimes it is better to just buy new hub and fan.

Lau parts makes a new super quiet fan design that also uses less power.
This fan series is called the Cobra Blade.
It looks like wild Klingon double bladed killing weapon.

Starting on page 23 here:

https://www.lauparts.com/-/media/la...2017BlowersPulleysWheels_REV08062020.pdf

A plain multimeter without a capacitance measuring position
can still be used with a clock that can measure seconds
to roughly find a capacitance value.
Google or youtube search for that.
You now have two “double” capacitor cases which have 4 capacitors that can be tested and compared with this method.

There is an old moparts post on doing this capacitance test with Harbor Freight “free” digital multimeters.

I had to replace ours for the first time last summer. The original did not say anywhere where it was made, nor does the replacement. The replacement is a TOTALINE brand which is the replacement components division for Carrier. It's a 40+5 MFD. Worked perfectly on our 16 year-old Goodman.

Thats how ours went out. I thought it was strange too.

Thank you all for the responses.

Today I finally had time to replace the Condenser fan and all is well.

Apparently the Capacitor and Fan went bad at the same time. After replacing the Capacitor, compressor & fan worked better but the fan was still bad.

All your help was much appreciated, without it I would still be in a pickle.

System is still crappy and old but your help bought me a month or two to pick the replacement system I want and not whatever I could get.

Depending on its age you might be better off fixing the old one. The new ones are cheaply made with thin copper tubes.

I am glad you found and fixed the problem.

Keep in mind with new HVAC systems:

1 The inside tubes of new evaporators and condensors have “cut spiral groves” that slightly save electricity but can greatly shorten the time before leaks come. Bad trade off.

2 Freon 410 is less efficient and as a mix of 2 gases more complex than older Freon 22 which is only available reclaimed and more expensive

3 New systems have more complex and costly parts and inherently harder to be reliable

4 New systems can be much quieter and dehumidify better

5 I am leaning toward two, three, four Minisplits rather than one central AC unit because
I do not want 100% of the cooling system down,
and I want to be able to use a smaller, quieter generator to run at least one cooling unit during sleep when the power is off.

I agree the long term dependability of the old stuff is probably better but this unit is undersized for the house and always was.
Besides having an undersized AC unit, I have had to clean the gas burner heat exchanger several times of rust which means that heat exchanger is 30+ years old and on borrowed time.

On a plus side to this system, in 30 years I have had to replace the condenser motor and capacitor twice. I also had to rebuild the drain tray under the evaporator, replace the condensate pump twice, several thermocouples, and the house fan motor once. No single part was more than $90 and was easy to replace. I do not think a new system will be so kind and that is why I hate to see it go, but it is time. Nobody has parts books that include it anymore, so finding parts is problematic when the labels disintegrated years ago.

Even though installing a new one is easy enough, I may pay someone to install it for the extended warranty.

Thank you all again.