This sounds suspicious to me. But, before you decide what you are going to do, we can work on some other possibilities, check out some things and then you can decide which path to take. Electrical repairs are tough, so don't get frustrated. It will work out.
Let me in on a couple of details so I can help as much as I can;
How much gas was in your car? Unless the gas was over 3 months old, that is not something that would stall a car out. Especially if the car had not been sitting for an extended period of time, Was this a suggestion from Honda? There is not a fuel tank drain plug as far as I know so they would have to pump it out. Then they would have to evacuate the residual gas in the pump, lines and probably have suggested cleaning the injectors. Don' hit them with questions about that first though, get a case file going so you can, interrogate them if you find enough evidence to warrant such action. I am only going with my experience and instinct. You will have to verify some things as well before really seeing if you have been swindled.
Did they take the car to a Honda dealership? Which one? First take the phone numbers they gave you and do a reverse phone number check which you can find on the internet.
The diagnostic tools to determine if the distributor is bad can be done with a multi-meter and visual inspection. However they would need the specifications to do that. There is a diagnostic tool called an OBD tester. Your car is OBD-2, which is the second generation of, "On-Board Diagnostic" testers in almost every car made and the testers are universal and generally less than $200. The codes would tell them what was wrong with the car, with some very small room for error, and the codes have to be looked up but they are very accessible. Most repair shops would have a higher quality OBD-2 tester which actually translates the code and actually describes the problem. In several languages:)
I am also concerned about the dash light that you see that is staying on after starting the car. Double check and make sure it is not the ABS light. They could have damaged it during, "whatever" they did to it and make sure that it is not the ABS light as that is something that is easily damaged if the battery is not disconnected during any electrical repairs.
Rasmataz is correct about the Crank Position Sensor, (CPS). They do have issues that could lead to ignition problems, which will keep the engine from running. It is also possible that the mechanics who worked on it might have mis-diagnosed the distributor as a failed CPS and were really trying to fix the problem. Keep these things in mind as you work through this since there are a lot of possibilities and diagnosing the electrical system in a car is very tough. So, make sure that you look and consider as many possibilities before we jump to any conclusions.
As far as replacing the engine goes, I would hold off and do some research, consider other possibilities. Since you have done a good job maintaining the car, I think it is highly unlikely that it needs replacement. Also, ask the repair shop how long they will keep the car without going forward with repairs until they start charging you any storage fees. Take this time too look for a repair shop, There are links to reputable repairs shops on this site in your area. Also, consider taking it to a dealership.
Yes, there are some, "suspect" things about the entire scenario, but hold off before making any judgments.
Keep me informed as I will keep this post on the top of my list and get back to you ASAP.
Take care
Monday, September 28th, 2020 AT 4:45 PM
(Merged)