1992 Oldsmobile Delta 88 Odd starting problems and sounds

This car was bought used a few months ago from a very reputable dealer.
From day one, the 'check oil' light was on, and always stays on, yet oil level at that time was actually ABOVE where it should have been. Lowering oil lever to proper level made no difference.
Now, however, as the weather has cooled, (or maybe in spite of it) it has developed a starting problem. My wife, who drives this car reported to me that "It won't stay running when I start it unless I put it in reverse, and then right back into forward, and then it will stay running fine" She also reports that if the does not do that, she must keep foot on gas pedal to keep it running. I tried this this morning, cold enough for frost on windows, and she is right. Also, it did not sound right to me, the engine sounded odd, (i know, that is a meaningless discription) It sounded like it was running either too lean, or was 'straining' in some way. Once I kept foot on gas pedal, it did stay running, but still did not sound right. If I did not put foot on pedal, it died instantly. I thought I would see if letting it warm up a bit would make any difference, it did not. But as soon as I put it into gear, reverse and then back into drive, then park, it stayed running fine, and sounded more like it should, running smoother, faster, and quieter. It then stayed running in park until my wife got in to go to work, about five minutes later. She reports this is the 'new normal' for this car. I suspect computer issues since it WILL run OK when one goes through the steps I've outlined. If it was a actual mechanical failure, I would expect it to be there all the time, or at least, most of the time, depending on what one is doing. (Foot on gas pedal, for example) We do not know much of the history of this car. It is high miles, over 100 thousand. Up to now, it has functioned flawlessly, other than the check oil light, which worried me.
I'm smelling a very expensive repair just around the corner, and, as we live out in the boondocks, and winter is almost here, and my wife has to commute about 30 miles to work, (one way) I am wanting to have this car as reliable as possible. I am disabled, so we do not have a lot of money. (And I can not do a lot of repairs myself) Which is why we bought this second Olds 98 used. (First one was from same dealer two years earlier, and is older, a 1989 and not as fancy, yet same motor and everything, It runs fine, other than the check engine light seldom goes out, never for long) At $1,200 for this car, I am unwilling to put a whole lot of money into it. (I can get another, newer, nicer car for not much more) Should I trade this car off while it still runs? Should I have a code reader put on it? (They charge about $30.00 to $50.00 just to hook up, and then say the car is too old to get a proper reading) I do have a repair shop I can trust, they do reasonable work, but it's in another town, and would mean the car is out of service for a few days, at best. Right now, my wife is needed at work more than usual, and can not be late or not able to get in. It means a lot of money, (for us, anyways) that she complete this project at work. (A promotion is hanging in the
balance) Any advice, suggestions, ideas?
Thanks in advance.
Chris aka TheRealJunkman@Yahoo. Com