My mom's 2001 Taurus SES has intermittent starting problems.

I had three years and 5 tows of experience with this problem. I spent $300 with so-called auto experts who gave up because they could not identify the problem. Over time I realized that it was a problem relating to improper setting of the transmission shifting mechanisms. Frequently, I noticed that the key would get caught in the switch and that problem related to improper placement of the shifter into park. It is apparent to me that if the shifter is not properly advanced into park, the starter will run but the fuel pump is not activated. Over the past year this problem has occurred only once and it was easily resolved by pushing firmly on the shifter to assure that it is fully into park. Now each time I start the car I pay attention to assure that the shifter is pushed up firmly into park and the result has been 100% starting. Prior to doing this the starter would run, the car would start and then quickly quit leaving a strong odor as a result. Continued attempts to start showed that the starter was fine but the fuel pump was not running because of improper seating of the shift rod. The best solution may be resetting the shift rod connections to the transmission but I am fine with just pushing up firmly on the shifter.

For a true diagnosis, wait till summer when its hot outside, and leave the car with the repair facility for as many days as necessary so that they can 'catch it in the act' to diagnose the starting issue. The car may have to sit for a week for it to act up once. But, when that happens, it happened to the repair place right underneath their noses.

Cover the starter when having an oil change. Had this same problem and cause was getting oil in the starter while having oil change.

My Ford Taurus 2001 had the same problem for several years. I finally fixed it by replacing my fuel pump.