I don't have power windows in my SL1 but looking at the schematic it looks like power to the switch, the motor and the two wires going to the motor are OK, otherwise you wouldn't see the window go down. It would appear that you have a faulty switch, the rocker contacts not quite making it to the "UP" position. If you have an ohmeter, you could check whether the contacts are making it. If you have a digital voltmeter, it will allow you to see the voltage going to the motor. In one direction it will show you +12 volts (approx) and -12 volts in the reverse direction. Be careful if you're measuring with an analog meter or you will pin the needle with negative voltage, just give the switch a little tap to check for movement. Measure accross the TAN and DARK BLUE with WHITE tracer wires. (Switch contacts 2E and 2F). I'm not sure if those switches can be disassembled, you could try taking it apart and cleaning out the connections to get rid of oxidation, corrosion, etc. I've been lucky with VW switches in the past but can't say whether the Saturn ones case be taken apart.
Otherwise get a replacement switch. Unfortunately you can't buy them separately. :(
Now... if you have good voltage leaving the switch (ie. +12 and -12) then your problem might be the motor itself or there is something binding the window and preventing it from coming up.