Problems with 95 Riviera Starting

For about two years now, my 1995 Buick Riviera has been fickle about starting. Sometimes it fires right up, sometimes it can take about ten minutes to start, and occassionally it won't start for over two hours. It turns over just fine, no slow cranking or skipping or sputtering or coughing. It's not the battery, the alternator (which has been changed three times), or starter. I've taken it in to two different shops and they can't find the problem.

Sometimes when we're riding along, the car just stalls out, like it's out of gas. Usually, it'll start right up again.

Also, the fuel pump turns off and on even while the car is off.

I'm guessing it's the fuel pump but the shops who checked it with their fancy computers say it's not the fuel pump.

The car turns over just fine. It's getting fire. So, it's got to be fuel, yes?

Also, I thought perhaps it was a security issue. Someone told me that her car (a different brand and model) did the same thing and she ended up changing a lot of electrical stuff under the dash, including the radio, and she hasn't had that problem since.

What could this be? The car runs fine after it starts (except when it just dies--it does this at any speed).

Hope someone can help! I love this car but I'm ready to scrap it if I can't find out why it won't start sometimes.