Car won't start

[Color-Hype]

Car: '89 240sx
Problem: When I turn my key, it cranks but doesn't start. This mostly happens in the morning after I leave it overnight. But on occasions, it'll happen a bit throughout the day. One morning I was late to work trying to get it to start, so I just caught a ride to work. After I came back from work, I hopped in and cranked it again and it started right up without problem. Other times it will start, but die right after with a violent shake. I'd need to push the gas pedal almost to the floor while cranking to get it to stay alive. I've read up about it and it seems as if my fuel filter is clogged or the fuel pump is going. But for reassurance, I ask the zilvia community.