1999 Chevy Lumina

It could be the crank shaft position sensor. They go bad sometimes when they get hot, then when it cools down they are Ok again. Not sure about the puurring noise. Does it sound like something is running?

Thanks!I did get the new spark plug wires put in today, which I didn't do when I got the spark plugs changed. So I guess we'll see what happens. The person who changed them, did put it t on the code reader, and the only thing that came up was MIL solenoid circuit.

MIL usually stands for "malfunction indicator lamp" which is the check engine light circut. Does the check engine light come on when you turn the key on? If it dosen't than that's why that code is setting.
Let me know how you make out with the stalling

No, the check engine light isn't coming on. When it did a while back, it was the mass air flow sensor that was bad. It stalled on me today. I don't know what is wrong at this point. The diagnostic machine isn't turning up anything.

Well if the check engine light isn't coming on that could mean one of two things. Either the bulb is burned out, or the computer is faulty. If the computer is bad, that will cause all kinds of stalling and other problems, and may not give you any codes in the meantime.
I don't like to throw parts at a car that I can't diag. Myself, but you may want to look into the crank shaft position sensor. Only because when they go bad, the car will stall and not start for a while, and they won't set a code in the computer on the older models like yours.
Also i'd look into the check engine light bulb, cause if the bulb isn't bad then you may have a computer issue.
Let me know how you make out with them and we'll take it from there.

Thank you. Will do.