Since the Triumph is currently on time out for being naughty and not charging it's battery like a good motorcycle, I thought I might ride the Vespa to work today.
Last night I went out the the garage to make sure the Vespa was still healthy and happy and likely to start come this morning. Sadly, it was not. The battery has caught a nasty case of "dead."
Incidentally, you can be certain that your battery is dead and not just very, very sleepy by doing an impromptu load test with your multimeter. You have a multimeter, right? If not, get one. Especially if you like European bikes. You can get a cheap one for practically free, and you will use it a lot once you realize how awesome it is.
Start with a fully charged battery. If you battery isn't charged, attempt to charge it. You have a battery charger, right?
Set the voltage test on your multimeter to 20 volts and turn it on. With the fully charged battery in your bike, connect the red multimeter probe to the positive battery terminal, and the black probe to the negative terminal. It should probably read somewhere over 12 volts. If it's less than that, and you just charged the battery, that's bad.
Anyway, turn on your ignition and see how much the voltage drops. It might go down a little, but shouldn't go down more than maybe one volt. Hit the starter button. If the voltage drops dramatically, you've got yourself a dead battery.
Of course, if you don't have a multimeter, and for some reason you aren't willing to shell out $5 to get one, you could also do the following: Try to charge the battery, and when it's done charging, attempt to start your bike. If the starter blows a raspberry at you, your battery is toast.
Now when you go to get your battery replaced because it's still under warranty, you can tell the helpful employee that you load-tested the battery and it is dead, so please make with the free replacement.