1989 Delta 88 Royale 3.8L V6 FWD 151,985 miles

To start. When I try to diagnose the problem, it goes no further than flashing "12" over and over again, that it is in diagnostics mode. I had needed to have my harmonic balancer replaced since last fall. I had not driven the car like this much--probably a few hundred miles. Now, to the problem I've been having with my car. About three weeks ago, after I had been out running errands and shopping for awhile, I got in the car, started it, and the car acted as though it were getting no gas when I pressed the pedal to the floor, and also backfired once. Eventually, it started accelerating normally and I was able to get home. Hoping this was a one-time occurrence, I next went to my parents' home. It had rained that day, and when I went to leave that evening, I could not get the car to start at all. I surmised it might have been because the engine was warm/dampness was affecting it. The next day, when I went back to get it, it was a sunny day and it started fine. It was shaded where it was sitting. (I though this may have made a difference.) Then I went to the store and left my car running, and barely made it out of the parking lot and home. It had to be restarted in the parking lot and I briefly had a difficult time keeping it running, once again putting my foot to the floor, giving it gas, and having it not go anywhere. St. Patrick's Day, I drove it a very short distance to park, and had no trouble starting it again when I left. Shortly thereafter, I had my harmonic balancer replaced. After this was done, it started with no problem. I drove it to my parents' house again, got stuck there again, went back the next day to get it, and it started and once again drove just fine. However, this time, when I went shopping for groceries, to stock up, I shut the engine off (I had my daughter with me the last time, it was a short stay, and this time neither was true). Surprisingly, I had no trouble starting, or driving, the car when I came out! My mother had suggested I go to a nearby auto service shop while I was in the area, to ask some questions re:analysis/diagnostics/ideas(battery cables?--Puhleeze). (It cost too much for me.) When I went to leave, it wouldn't start. It ended up being stuck there for almost three days (sitting in the heat/sun, no shade) until my brother went with me on the third day to try again to start it and used starting fluid in the throttle body, which worked. And it was cloudy that day. The problem seems to be a function of distance/time driven/something getting hot, because if I drive it short distances, it is fine (although I don't shut the engine off anymore, just in case). My brother, however, did get it started again (at home) after it had been driven and was hot by cranking the engine and pumping the gas until it finally caught and ran, but it sounded odd, like it was not running quite right. I know that if I drive it any real distance at all, (how far is hard to say--maybe over 2 or 3 miles, but maybe it just needs time to cool down if I drive it shorter distances?) I can't shut it off, or it won't start again, until it has had time to sit overnight in a cool spot, like my garage/basement, or it needs to be cool, or it can't be hot in the first place. I backed it out of my garage yesterday and couldn't get it restarted at first, but let it sit for awhile and it was fine. I tried to start it with starting fluid and it would not start. Now, that one I can't pinpoint at all, because I only backed it out of my driveway and pulled it back in. I sure hope you can tell me what's wrong, because my brothers and dad have their intelligent guesses (something is getting hot, or it's the computer brain, or the cam shaft sensor) but no real answers. Help!