Hello,
I know TXgreasemonkey is so knowledgeable, I'm hoping I might get some advice..

My 1995 Honda Civic (75K, 4 owners, manual) started missing and sputtering about a year ago. This was a few months after I'd drained the battery completely leaving the lights on in long term parking. (I replaced the battery) So I replaced plugs and the air filter. Car improved, but then stalled at high speeds. I did not drive it much until I replaced the fuel pump. Again it did well for awhile, then the problems came back. I had the distributor replaced, and the same story. Then it started stalling while stopped, but it would start again. The Check Engine Light was not coming on. This morning it stalled, the CEL came on for a second and went out immediately. It would not start. It was cranking, an I thought I could hear the fuel pump. I couldn't even jump start it.
Help?

My car usually shuts off whenever the module in the distributor was burnt. But you need to confirm this by proper diagnosis.

Remove and fully charge the battery. Most auto parts stores will test and charge batteries for free. Don't jump start modern-day cars--there's too much risk that a voltage spike will fry your ECM, alternator, and sensors.

If the Check Engine Light comes on and goes off after two seconds, when you turn the ignition switch to ON (Position II), and you can hear the fuel pump run, then the problem is with the distributor. Over 50% of new aftermarket distributors have not worked out of the box, at AMHD. Of those that worked, many did not last long.

Check the warranty on your distributor. I suspect one or more of the internal sensors (CKP, TDC, or CYL) have failed, which are not serviceable. I only recommend using a genuine Honda distributor housing, where it's fine to install an aftermarket Ignition Control Module and coil to save money. A bad distributor is responsible for all of your performance and reliability problems.

After installing a new distributor, remove the 7.5A BACK-UP FUSE, in the under hood fuse box, for 10 seconds. This will clear any codes and reset the ECM.