[papajam]

Disconnecting the battery to check the charging system is, unfortunately, a common practice. The battery acts like a capacitor. If disconnected, wild voltage spikes can occur that can burn out kinds of electrical stuff; light bulbs, computers, etc. A volt and/or ammeter is the most accurate, and safe, way to check the charging system when the engine is running.

First thing I'd check is the fuses (usually #6, but depends on the year). Make sure that they are clean and tight. Then disconnect the battery (negative side first), and check the connections at the alternator and regulator. If the alt light still glows, then the alt or reg may have been damaged.

Good luck!!