Why would my car turn on then right back off?

The other day I was running errands and I turned my car on, it turned on, shook, rpms went up and down quickly for a sec, and then it shut off. I tried it again, and did the same thing. I then waited a few minutes and it was good to go. I took it to the shop and they said my battery was at 9% and my belt was wore out and replaced those items. However, it has done this shut off-wait-good to go thing twice since. It is only happening when I have to start it up and turn it off several times in a short span. I have no indicators on with the exception of an emissions light that has been on for years because of a faulty o2 sensor. I've had the car in several times over the past few months because it tends to idle high for a few minutes when first start, and for a bit, I suspected an issue, maybe a misfire in the first cylinder. Each time they've been unable to identify a problem. The car is riding smoother than it has in a long time, and drives well once its on. Sometimes there seems to be a hesitation in acceleration, but that just could be my paranoia. Any ideas? Car is an 01 Taurus by the way.
 
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