I noticed my battery taking a little longer to start so I decided to change it before it quits on me (it's 4 years old). So I got a new one, same specs and all, but when I hook up the negative (-) cable the horn goes off, as if the alarm had been triggered (factory alarm), and won't stop. This happened again when I put the old battery back in. So I left the old battery in and took out the horn fuse, noticed that the blinker lights were still blinking, and then tried to start the car, but it wouldn't start. It's like there is no power going to the starter because it doesn't click, the engine doesn't roll over or anything, but my auto-lock doors work, cd player works, maintainence lights, everything but the starter. My friend suggested maybe there's a switch to flip to reset when the battery is changed, but we don't know where it might be, the guys at a shop said maybe the computer needed to reset, so wait 5-10 min before trying to start, so I waited and it still wouldn't start. Any suggestions?

I don't know if this will work. But, try locking the driver's door with your key. Wait a minute or two, then unlock the door with your key. Now, see if it will start. Sounds like the alarm is disabling the engine. Is there an alarm key FOB with that car? If there is, you could try resetting the alarm with that, too.

My car has a remote keyless entry key, which I tried every button while the alarm was going off, but nothing happened, it kept going off. I also tried starting it with different keys (orig./remake), but nothing worked. It didn't even lock or unlock the doors. After about 10 secs the alarm seems to stop (the lights stop blinking), but when I push the buttons on the key the lights start blinking again (I have the horn fuse out).

Your alarm thinks someone has cut power to disable it.
When power is re applied (from any battery) the alarm will go off and disable the car's starting circuit.
Pulling the horn fuse will silence the horn only, you need to turn off the alarm so it recognizes you as an authorized owner.

Thanks. I called a toyota car dealer and they told me the same thing. They said to reset the alarm with the key and then start, and it worked, so thanks everyone for your help.