How do I diagnose when a new battery is needed?

I have a 1993 K 1100 LT with 39,000 miles. I have only had it for 6 weeks, and put about 400 miles on it. Up until last week, it started immediately every time. I did notice the battery light flicker on a couple of times when I first started it, but last week, after starting it and runnig it for a couple of minutes, I turned it off. When I tried to restart, I had nothing. I jumped it from my car and it started, but after running it a couple of minutes and disconnecting the cables, it immediately shut down again. I did notice that when it was running while hooked up to the cables, the headlight wasn't working. Does this suggest a charging problem, or could it be a battery?

Used bike = new battery
Old battery = 24 hours on a trickle charger

Check all your connections.

Either way, start from there before you start trying to diagnose the electrical system.
Voltmeter should tell you right away where you stand.

Do the tests in this order.

To test the charging system:

Put a voltmeter on the battery terminals and start the bike with a jump start or after charging the battery with a charger.

As you rev the engine, you should see the voltage rise from ~ 12V to 12.8 - 13.5v. If the voltage does not change much, then your charging system is suspect.

To test the battery condition:

Charge the battery with a charger until it is fully charged. This should take no more than 6-10 hours, depending on the charger and initial battery charge.

Disconnect the charger, wait 10 minutes and check the battery voltage. Wait a day or two, then measure the battery voltage again. It should have dropped only a few tenths of a volt. If it's more than this, your battery is not holding an charge and should be replaced.