1997 Mitsubishi Eclipse Eclipse won't start

We bought a 97 Eclipse and drove it for 1500 miles. Now it won't start. We replaced the fuel filter and it stared right away. The problem returned the next day. We replaced the fuel pump, an the car stared right away again. The next day it wouldn't start again. We replaced the plugs, and put in a new battery. The problem persists. The car turns over fine, will breifly fire when the iginition is first engaged, and then it will just spin and not start. What could be the problem?