First of all, cimerio, welcome to the forum : )
Another thing you might try, if cleaning with alcohol doesn't work (and again, make sure you always keep the head pointed UP, as in the LED facing UP, you don't want liquid getting down in the head), is to try using baking soda mixed with a bit of warm water, mixed so that it's a bit looser than a paste, but not watery.
This mixture is VERY good at neutralizing battery corrosion, then follow up with the alcohol cleaning again. I've saved many of my friend's Maglites that had batteries so corroded that we had to drill them out first.
And finally, just to echo the others, use this as a learning experience to NOT use alkaline batteries in your lights.
Anyway, good luck, and let us know how it turns out : )