First of all, does the engine turn over at all when you turn the key? If all you are getting is a clicking sound, then you either have
a)bad battery(which you said you have eliminated)
b)dirty battery post terminals
c)bad starter motor
To fix these problems do as follows:
a) bad battery-try charging it for a couple of hours or you can also try a jumpstart
b)take the terminals off the posts, clean them good with warm water and baking soda, then clean both posts and terminals with a wire brush. Put a bit of grease on the post to prevent future corrosion.
c)You will have to follow the positive battery cable(the big one) down to where it attaches to the transmission/engine and take it out and either get it rebuilt or buy a rebuilt one from an auto parts store. Most places will test your old starter free of charge to make sure that is/not your problem.

If the engine just keeps turning over and over and won't fire, you open up a whole other can of worms. It could be MAP sensor, distributer, coil, fuel pump, the list goes on. Did it rain last night where you live? Somthing may have gotten wet.
Good luck and supply anymore info you can.