It sounds like it could be a bad battery, or a bad ignition switch. But you must go through some quick tests. Bear with me, I don't know your experience level so I may be more detailed than needed.
The first thing you need to do is check your charging system, to eliminate -or include- the alternator, battery, battery terminals, etc. as part -or all- of your problem. I'm assuming the starter is good because once you apply sufficient power (jump start/boost) it always cranks.
In place of expensive shop equipment you could use a basic home multimeter and 12V automotive test light to perform many tests.
1) Check the battery terminals: Side Terminals normally corrode under the rubber covering on the positive side. Check this carefully and clean them. If you see any corrosion then you have to pop the rubber off to get inside, I usually cut it open on the top side to get the bolt out and clean it well. I dislike the side post battery as they cause many problems, but you have to work with what you have. Check both Pos and Neg terminals for a tight fit and good clean connection, clean/repair as needed.
2) Check the Battery:Set multimeter to read DC volts and check battery between Pos and Neg terminals. It should be just over 12Volts(12.1-12.4). If it's lower than 11.5 volts, have it tested at a shop or auto parts store, preferably after you charge it. **If it tests too weak(even borderline OK) replace it now.
**Note on Battery replacement:Even if the battery is bad it may not be the whole problem, but you can't go any further until you replace it. You can't properly diagnose starting/charging issues with a bad battery.
3) Check for a slow drain on your battery: You will need a regular test light for this.
Remove the negative battery terminal and push it asid so it doesn't touch battery post. Put one end of the test light on the battery neg post, and the other end on the neg battery terminal. You are basically jumping a test light between the battery and terminal.
All doors must be closed, key off, and if there is a hood pin(factory alarm or other) it must be depressed as if the hood was closed. If test light is lit up at all (dim or bright) then you certainly have a drain. Dim is a slower drain than bright.
To determine which circuit is open/short and is causing the drain, you must first secure the test light in that position because you have to remove fuses and can't hold it while doing so.
Tip:A short 3/8 inch bolt screwed snugly into the battery neg post is a good way to clip test light on the battery end. Now you only have to secure the other end of test light to the negative terminal. Just make sure you have a good connection on both ends.
Your car has two fuse blocks, on left side of engine compartment and behind center of dash, go through every fuse.
With doors closed, key off, hood pin depressed, pull one fuse at a time and watch for test light to go out. If it stays on replace fuse and go to the next one. If you can't keep one door closed while removing inside fuses, that's cool. Remove the fuse first and then close door, see if light goes out but allow a few seconds between all fuses for the interior dome lights to go out or the light will be lit from that.
When light goes out you just found the Circuit that's causing the drain. That eliminates a sh^tload of time looking through wiring and sytems that are unrelated to your problem. You may have a multiple circuit that powers a few items or a simple circuit that powers just one. Now that you know the offending circuit you must go trough it and find the short/open. At least you narrowed it down.
4) Check the Alternator: The voltage numbers posted are a guideline only, but should be very close.
Start this test with new battery or tested good battery. Set your multimeter to read DC voltage and take a reading between the Neg and Pos battery terminals with engine running at idle speed. You should read somewhere between 13.4V-14.3V. Be advised that a really bad battery could drop this number down into the 12 volt range which is why you have to be certain the battery is good or you are wasting time. I keep harping on that point for a reason. Do this test with lights, accessories, etc. OFF.
If you read roughly 13.4V-14.3V then the Alternator is good.
If you read lower than 13V with motor at idle you have to verify that the battery is good (if you haven't yet done so). Before going further, rev the engine and hold it at 2500-3000-rpm while reading voltage at battery terminals with multimeter to see if the voltage goes up to normal, if so the Alt is good and you have a bad battery. Test and replace battery. If battery was found to be defective, check charging system again (at idle) with new battery installed. It should read normal range(13.4V -14.3V) if lower then alternator is BAD. ETA: Damn, I seem to be repeating myself
5) Saturn issues:The Saturn SL1/2 and SC1/2 in particular are very dependant on a good battery for the alternator to do it's job. Other cars may get by with a halfway decent battery, but the Saturn won't. Many mechanics will diagnose a low Voltage reading (at the battery with motor running) as a bad alternator, and they would be wrong and would have the same problem even after replacing alternator. That is until they put a new battery in the car.
6) Ignition switch:Troubleshooting the switch is too complex to post here, if everything above is in good working order and has been replaced/repaired as needed and you still have a problem, the Ignition Switch is probably bad and should be tested using a manual or have a shop look at it. The sudden loss of power is one of the major symptoms of a faulty ignition switch, but as I said the other things must be donw first unless it's clearly a switch, and without being there I can only put you through systematic troubleshooting procedures.
Good Luck and keep us posted.