Weird fuel pump problem.
 

So I spent the entire day trying to fix this, and this is what I have so far. I have a 2001 Tiburon. Three days ago, it wouldn't turn on, but a quick wiggle of the battery cable made it work. Same thing the next day. Today, it wouldn't turn on at all. The battery and the starter weren't the problem, so I figured it was a fuel system problem. I tested the fuel pump relay and checked the filter and both were good. I checked to see if the fuel pump was making any noise when the key was turned, and sure enough it was not. So I took the pump out. I connected the pump to direct power, and it worked fine. I plugged it back into the harness, turned the power on the vehicle, and the fuel pump did not respond. I took out the fuel pump relay and jumped it, and the fuel pump turned on perfectly. So now that's where I'm stuck. The relay is good, but for some reason it is not sending power to the fuel pump. I've been reading online and some people say that it may be the ECU relay, but none exist on this car. It has ECU fuses, and both are good, but no relay. Please help.

If you wiggled the battery cable and it worked, why would you think the problem is with the fuel system? Did you think about replacing the battery cables? Just because the battery and starter are good doesn't me the cables connecting them are.

It was the pump. That is a fact. But now the pump is working, and the car still won't start. We found that there is no spark reaching the spark plugs. There is voltage all the way up to the coil, but it's not getting past the spark plug wires. Could it be the ecu?? We figure it is since both the pump and the spark went out at the same time.