1999 Dodge Caravan oil light

This question is about our computer and the oil light. First some background. About 10 months ago, according to our mechanic, our 1999 Dodge Grand Caravan had a computer that didn't work. He said it would cost $500 to fix, but we could just let it be and accept the inconvenience of some things not working. (We wanted to save some money because we had just paid for a rebuilt transmission.) We noticed 4 things wrong: the airbag light is always on (he says that means it's disengaged), and our horn and cruise control don't work, and the service engine soon light was always on. We've driven it for the past 9-10 months like that, including moving to a new state.

About 3 months ago, we had to get the water pump replaced, and asked our new mechanic about the service engine soon light. He checked it, and said nothing was wrong, and re-set it so the service engine soon light went off. It came on a month later and now stays on all the time again.

About 2 months ago, our oil light came on intermittently, sometimes with a few chimes. I checked the oil level, and it was low, so I put more oil in. It seemed fine after that. We drove it for the next 2 months and it seemed fine. But just the other day, the oil light came back on and the chime returned. The next day, I checked the oil level, and this time it was full. We drove the car a short ways on the next 2 days, and there was no oil light and no chime. My question is, with full oil, can the oil pressure still be bad? Why doesn't the oil light stay on if it really is a problem? Can the oil light be merely another ramification of the broken computer?