I really hope you can help me with this one. My '93 Buick Century has a problem. The battery goes dead after about a week. The first time I brought it to my regular repair shop they put in a new battery. After two weeks it was dead again, so this time they replaced the alternator and charged the battery. I only made it a week this time.
Sounds like an unwanted amperage draw on the system, assuming the new alternator and battery are functioning correctly. It's like leaving your headlights on, but you can't turn them off.
Check the simple stuff first. Try opening the trunk just a crack to see if the light is on when it shouldn't be. A bad trunk light switch can do that, and the same applies to the under-the-hood light. Also, take a look at the glove box and center console to see if there is a glimmer of light shining through the crevices of the closed doors.
Next step involves a 12 volt test light, which is a simple tool used for checking circuits. But first make sure all lights are off, doors closed, ignition off, and disconnect the light under the hood. Then disconnect the negative cable from the battery. Put the alligator clip end of the test light to the terminal, and the probe end of the test light to the cable you just removed, or vice versa. Technically you just created a "series circuit". If the test light lights up, that indicates a draw on the system, assuming you turned everything off. If there is no unwanted draw present, the test light would be dark and activating any circuit (opening a door, turning on the interior lights) would light it up.
Now we begin to narrow down the cause of the problem by pulling fuses. Get to the fuse box, but do not leave any doors open because it will camouflage our real problem. Start removing fuses one at a time while keeping an eye on the test light. When you remove a fuse and the light goes out, that's the circuit causing the problem.
Let's say it was the "courtesy lights" fuse that turned off the test light. Put the fuse back in and reconnect the battery. Now go around and double check anything that might be on the courtesy light's circuit, for example, interior lights, trunk light, center console etc. You may also try disconnecting suspect components one at a time.
If you haven't found the problem by now, you're getting a little too deep and the job requires a qualified technician with a wiring diagram to find the problem. A short, or perhaps a solid state component gone awry, may amount to a tough diagnosis. Maybe starting fresh with another repair shop would be a good idea.