1987 Honda Accord wont start - sometimes

Thanks raz. I have been waiting for it to mess up again so that I can test it. But it has not. I have figured out that every time it did not start I was on a incline. I am betting on the fuel pump at this point as I was told that there is a balance feature in the fuel tank that prevents starting if the car has been flipped or rolled. I have a starting point and simple diagnostic thanks to you.

As far as the belt. I will recheck the tension.

Thanks for all your diagnostic help.
Turns out it was getting spark, was getting fuel, noid check ok on the injectors.
ECU?
Here is my new question:
the existing ECU is part no: 37820-PJ0-666
it is listed for a prelude. I have an accord lxi
will part no: 37820-PJ0-665 work instead of the 666?
Thanks!
Btw, dealership said this one does NOT need flashed.

Thanks! That was a fast response!
. Guess it wasnt the ECM. Found an article online that describes the events with my car over the last 3 years perfectly.
"Why doesn't my Honda or Acura start sometimes? The main relay is famous for stranding people for a few minutes usually in a parking lot in hot weather. The problem is so common that it's been coined the "petrol station fuel relay" from fuel station attendants. The technical name for the main relay is PGM-EFI Main Relay Assembly. PGM stands for programmed, EFI stands for Electronic Fuel Injection."
I replaced the ECU/ECM after being assured from a trusted Honda mechanic that the last digit difference was ok. Still didnt work. Then I found the above article.
Now I just have to figure out how to get a socket on the bolts to remove it. And try that.
It has gotten to the point now that it will turn over but not catch. All the time. I cannot start the car. I love this car and I want to get her working again.

Well, that did it. I replaced the main FI relay and that has got her back up and running.
Thank you all for your help and interest.

Now I have a ECU that I dont need. Guess I will try and sell it.