Saturn 2002 SL2 No Start - No Electrical

I have a 2002 Saturn SL2 Automatic with ~56K miles bought brand new back in Dec 2001. Recently my car won't start and here is what is happening:

1. Car is in an insulated garage and so far the mornings in Colorado have been in the 20's (garage around 40's). This started on Monday. I would turn the car over and it would start then die. Do it again and it started but the service light and security light stayed on.
2. Drove the car to work (20 miles round trip) with those lights on and made it. Started right up in the parking lot with no lights staying on and was able to drive home fine in the evening. Everything good until Friday.
3. Friday morning I tried to start the car and it died after turning over. However this time when I tried to start it again, nothing. No headlights, dash lights, dome light, but the radio clock (Saturn factory CD player) was still on (though the radio wouldn't turn on). While the car's ignition was in RUN, the clock on the radio disappears.
4. I jump started the car and it started right up. I left the car in the garage and when I came home 9 hours later it was dead again, wouldn't start and the radio clock was gone again.

I removed the battery and took it to my dad's where he charged it all night. I then took the battery to Wal-Mart (where last Dec I had bought a new EverLast) and they said it was fully charged and working. I put the battery back in and it started up. I run it down to AutoZone who says the Alternator is good and the battery charged. They found no codes when running a diag. When I shutoff the car and restarted it, the Service and Security lights came on and stayed like on Monday. When I got the car home and tried to restart it, it was dead again. I found any load I put on when the car is in RUN (trunk light, dome light, headlights) will cause the radio clock to disappear and when I turn the car off, the clock came back on.

The only work done on the car recently was back in June a DCP (?) module was burned out and replaced. When this happened I had gone to the doctor's office where my car wouldn't start at all. It seems similar to this but I didn't recall the radio clock fading in and out, just that the fuel gauge would 'rise up' to the fuel level when left in the START position.

The guy at AutoZone said to check the sparkplugs and a friend at work mentioned the inline fuse or relay switch could be bad. Could I just have a bad battery? Any suggestions or experience with the above? Thanks!

Do you have a volt meter? Test the battery voltage while disconnected from the car. A fully charged battery will give a voltage reading of about 12.6 volts or better. Connect the battery and test the voltage again. Should still be at 12.6 volts or somewhere very close. If it is lower and dropping, you have a short somewhere. If it stays steady, have someone attempt to start the car while you again observe the voltage. If, when they touch the start position, the voltage drops like a rock and the starter doesn't engage, probably a shorted starter.

Did Wal-Mart do a proper load test? Did they check each battery cell with a hydrometer?

My neighbor came by this evening and we checked out the battery with his reader and it shows good around what you specified. He pointed out some pretty nasty corrosion on the positive connector. I removed the connector and cleaned it off with baking soda and water and it cleaned up a lot of the corrosion. I reconnected the battery and she fired right up. I repeated starting the car a few times waiting a few minutes in between and she fired up each time. I will know more in the morning.

Thanks for the insight and the reply!