Here is my problem: My engine starts and idles fine. Under acceleration it accelerates up to about 2500 rpm, then the ignition cuts off. When you shift gears you can run it back up to about 2500 rpm again, then it cuts out again. This occurs through all the gears. The check engine light stays on and I can not get it to read any codes. Any suggestions would be greatly appreciated.

Likely a bad main relay or igniter (ICM). Because of the age of your Civic, I would replace the main relay, igniter, and coil. RockAuto.com has the best prices, I've seen, on the main relay and coil.

When you turn the ignition ON, does the check engine light go on then off? Is there a relay click sound when the light goes out?

Thank you. Being perfectly honest, I have to find out information about the main relay. I don't know what that is. Where will I find it? The check engine light does come on, then goes out, and comes back on again as you run the car a short time, then stays on. I haven't noticed a clicking noise. I will listen for it. Should I hear it, what are your thoughts? Thanks very much.

Hopefully, this site will help:

http://techauto.te.funpic.org/civicrelay.php

In a properly running Honda, the Check Engine Light will come on and go off after 2 seconds, when the ignition is turn to ON. During this 2 second period, you will hear the fuel pump run. When the key is turned to ON, you will hear the first relay click; when the Check Engine Light goes out, you will hear the second relay click. The main relay is really composed of two relays.

On Hondas, it's good to start them in two steps. First, turn the key to ON and observe that everything is working OK; i.e. CEL comes on and goes off, which means the computer has check everything out OK up to that point, and that the fuel pump runs and pressurizes the fuel rail. Second, turn the key to START and observe how it fires off. Normally, Hondas will start faster, if you follow this short procedure, and keep you atuned to what's going on. Very important diagnostic information is gleaned from this procedure.

Be advised, however, you are on borrowed time on your ECM (computer). Many of these are starting to fail, due to heat and vibration, on older Civics. My advice, if you plan on keeping the car for a long time, is to replace it with a remanufactured Cardone ECM, with a lifetime warranty, from O'Reilly Auto Parts for around $275. Then, you start fresh on the significant electrical parts that give trouble. These cars can go 350,000 miles, if you take care of them. Yes, things like distributor bearings and radiators will have to periodically be replaced, but it's still good, cheap transportation.