Get a multi-meter, switch off the engine, check the battery voltage, it should be between 12 and 14 Volts. Pull the first fuse out, and see if the figure drops. If not, replace the fuse, and pull the next one, and repeat until you see a small rise in the Voltage - you have just pulled the fuse on the guilty circuit!

Multimeters cost only a few dollar$, and are a great tool to have.

X2 on what Ryan said. First you need to insure that your battery is fully charged. Just jumping it and driving it to work will not charge it enough to start when you get out of work. If you are sure your battery is fully charged and holds charge, then you can look to the alt as the next possible cause. If you can't get to a shop to charge it, you can disconnect the negative cable, this will store what power is in the battery, however, it will clear your stereo/miles memory.

"What can be disconnected to stop this?"

- The battery cable.

You may have to get it checked by a mechanic, but if you have an aftermarket satellite receiver that is always a major suspect.

You could have a bad alternator.