My Grand Prix is having trouble starting.

My 1999 3.8L Grand Prix doesn't seem to want to start sometimes. It happened just
recently at 198K miles. The first instance, my tank was low on gas, just enough to not
have the gas light come on, and it took pumping the gas pedal while repeatedly turning
on the ignition. I had to keep up the rpm's and then put it into drive, otherwise the
engine would die. The next day, it did the same thing before I was able to get some
gas into it (as I expected it would). The problem seemed to be fixed with a 3/4 tank of
gas. Then the next morning, I went to start my car, and again, I had to repeatedly turn
the ignition and pump the gas to get her going. Albeit, the latest time, was easier than
when the tank was close to empty. Another thing I notice is that once I her out and
driving, restarting her is no problem. It only becomes a problem after an extended
period of sitting. I want to think the fuel isn't getting to the engine like it should once i
turn the ignition. Any help on what this could be would be greatly appreciated.