1990 Buick Century battery won't charge

Welcome to the forum, If your saying the starter won't crank, I'd have to be sure the battery has a full charge and the connections are good. Next, I'd have to check the charging system.

Use a digital multimeter, place leads across the battery posts, everything turned off. Around 12.6 volts is considered a full charge. Start the vehicle, take a second reading across battery posts, the second reading should be higher than the first, if the charging system is working. If it isn't charging, possible wiring circuit fault to or from the alternator, or faulty alternator.

Another possibility is excessive battery drain, with everything turned off.