Your engine needs compression, air, atomized fuel, and healthy spark to combust. You can pretty much rule out air since that would make all cylinders misfire, and would have an associated code when the O2 sensors trigger. You can have fuel, but you need atomized fuel to be exact, since liquid fuel doesn't combust, that would have to come from an injector that is working the way it is supposed to be working. It can leak and that would be liquid fuel, it could clog and that would be low fuel, and can come out uneven and not enough to make a full combustion.
You could have a spark issue where either the spark plug or the coil is faulty, which is easy to check by the method I describe above. It is free and easy. Actually only need a few tools. Spark plug socket, ratchet, and extension two 2" extensions, and a 10 mm socket. Preferably a torque wrench but most don't use them. Just swap them around and see if the problem migrates. A compression test is also simple, if you can remove the spark plugs you can do a compression test. Just need to disable the fuel injectors by removing the relay, and remove the spark plugs and screw in the compression tester, which is cheap at harbor freight. Crank the engine over 5-6 times and the compression tool will hold the compression for you to check. This will tell you if it is a problem with the piston rings or valves. Put a little oil in the spark plug tube hole, and check the compression again and you can see if it is the piston rings since it will temporarily plug the rings and raise the compression if even a little bit. If no bump in compression it is the valves.
He could have even got the timing off. You have to line up the front and rear cam to the crank, and this can be challenging for some. You can run it off 1 tooth, but it isn't good for the long term health of the engine. You can have the crank and the front cam on and the rear off, or the front off, or the front and rear cam can be timed together, but the crank off. The marks can look off if you are not looking at them dead on. If you look at them from any angle, it will look on, but be off.
I hope he didn't use a cheap ebay brand timing belt that says it is Honda, but is not. The material is too weak and can stretch easy. This will give you off timing, and in a day to a few months they just fail. Some can go longer, but it depends on the driving habits. They are made from inferior material and have cost many engines their lives. Couple that with a bad timing belt tensioner and either one can fail in less than a year.
It is unfortunate that he was able to get this far. The first red flag was that he had to take the heads off to do what a simple compression test would have told him. From there it just goes downhill. I actually wonder if he even knows how to do a valve lash. It used to be a common thing way back in the day, but Honda is one of the few that still require it, and they are the few sticking to the rubber belts. Not to mention the interference engines. All 3 are engine killers.
Why don't you buy the tools to check these things yourself?
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You can use the universal joint in the kit, or get an extension kit like the one below. The issue is you can't get the long extension down the tube with the spark plug socket, so you have to put the socket with 3" extension down the tube, and attach the second 3" extension after, or you can try to get the swivel extension to maneuver down the tube.
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Amazing deals on this Quick-Connect Compression Tester at Harbor Freight. Quality tools & low prices.
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A few things to note. Remove the #R2 Relay under the hood relay box (Check video). Crank the engine until it doesn't start and run. Remove all of the spark plugs. This would be a good time to send us some pics of how they look. With the spark plugs removed install the compression tester on #6 and #5 cylinder. Send us the readings.