Everything you described in the original post is symptomatic of a discharged battery or poor connection / corroded battery terminals or cables. I've experienced all of them after the "auto-turn-off" headlights forgot to turn off

.
I have an '05 and have also noticed the rate of battery terminal corrosion buildup is worse than any other car I have owned. I clean it off with baking soda every year. This is usually caused by overcharging (which is an alternator problem).
The factory negative cable lists for $15 and you can buy it online from a dealer for ~$10. The positive terminal ass'y lists for $26.41 and you can buy it for $20. So we are not talking about a big expense here. Two or three companies make all of the auto batteries sold in the USA, so just go to Sears or WalMart and by the biggest one that will fit in the tray . . . should be less than $100. You could even offer the installer $50 to replace your terminals while he/she is at it. The welded-on terminal can stay attached to the old battery.
As MAToyotaSales suggested, it is probably a coincidence this all happened during an aborted start (though I admit I've never actually tried it myself, and are not inclined to).