If it "Overheated pretty bad".. How long did you run it overheated?
Has this been running 'hot' for a while?
When was the last time you checked your battery? How old is it?
When was the last time you/someone flushed the system?
Acid doesn't evaporate, its' the water/electrolytes that do.
If the battery got overheated, (for long periods) you probably cooked it.
It doesn't take much for the plates to warp and if they touch one another, they kill that cell.
Just because it states "maintenance free" doesn't mean that it shouldn't get checked and that it won't need water ever.
Get a new one..
NOW, for the engine. Is there water in the oil?
White/grey smoke came out the tailpipe?
After you put another NEW battery in, pull the plugs and try and turn it over.. Does water blow out of one or more holes?
Honda motors can handle tons of stuff except peeps that don't take care them.
E