Modern Vespa

OK I did a bad bad thing. I needed to recharge my battery but I left the ignition on durring the charge. Now I get nothing. Anyone know what I've done?

You need to do some investigation on your own that we can't do for you. Start with the easy things. Check all your fuses (not likely but easy to check). Get a multi-meter and read the battery voltage with the charger disconnected and the ignition turned off.

-Craig

If your headlight is on with ignition on then your battery is probably dead.

Even if the headlight doesn't come on with ignition on, the standing current of a GTS300 (say) at ~2A is more than a battery tender can provide - ~800mA.

Either way, try re-charging without igniton on - you might need to jump-start the bike first from a car and run for a few minutes (then off again) to give the charger a chance with some volts showing. But my bet is the battery is now compromised beyond sensible reincarnation.

I'll try the recharge and the other test.
Could I have damaged the electrical system

If yuo have access to another battery..try it.

Battery reads 6.5 v.
Charger is dead.
I'll have to get a new charger and see if I can get the battery up and go from there.

6.5v? You've killed it. Cut losses, get a new one, and *do* charge it first, regardless of manufacturer's claims.