just put in a new 12v battery but when I try to connect the ground cable, I'm getting sparks, indicating a current draw. And the horn starts blowing nonstop.
A moderate spark would not concern me, as some ECUs remain powered up at all time and your cabin lights may be on. Normal quiescent current draw should be around 20 mA when the car is IG-OFF and all cabin lights are off. I assume you have an aftermarket alarm installed. As soon as you connect the battery, do the normal process to turn off the alarm. If you don't have an aftermarket alarm installed then I have no idea why the horn would be blowing. I suppose you'll need to disconnect the horns in that case, to give you time to figure out that problem.
Uhh, which new 12V battery: the correct Toyota 12V battery, or something else? Note that there is no direct aftermarket replacement for the OEM battery; all substitutes require some modification to the cables, the mounting, or both. Especially confirm that the polarity is not reversed. The ground/chassis connection is supposed to go to the negative battery post.
I installed the correct Toyota 12v battery. connections are correct. So still can't figure out where I went wrong. any other suggestions?
I just bought the car from original owner; no aftermarket alarm installed. is the horn easy to disconnect?
If you look at the front of the radiator you should be able to find two horns. Just disconnect a wire from each horn.