Simply replace the computer, which is called the ECU, with THIS PART
It's priced at $69 and there is a best offer. No need to rebuild the computer.
If there is no change, you can sell your old ECU or the new one you got and recover some of the cost.
If you wish to replace fuel system parts, you can replace the injectors, injector resister, wiring harness, fuel rail, fuel pressure regulator, fuel filters and the fuel pump.
However if the Honda shop diagnosed the ECU as a failure, then replace that first.
Additionally, if one cylinder is not firing, change the injector from that cylinder to another cylinder that is working and see if the problem moves. If it does, you have a bad injector. If not, possible a wiring connection. At any rate, replace the spark plugs and plug wires to see if that "wakes up" that cylinder.
It sounds to me like a full tune up will take care of this problem. However, it may take some patience to sort it all out.
Good luck, let us know