When you mention one of the battery caps missing I'm assuming you mean the little plastic babies that cover the battery posts?
If you can't remove the clamp from the battery terminal then the only thing left to try is the old Coke routine. Get a can of Coca-cola & gently pour it over the corroded terminal. Wait a while & do it again. Drink some while waiting.
Try starting the car.
The best way, obviously, is to remove the terminal from the post & using anything (file, sandpaper, a pocket knife, whatever) to clean both the post & the inside of the terminal/clamp. A corroded terminal (usually the positive + one) will absolutely prevent your car from starting & since these cars are electrical hostages, will also cause all kinds of other bizarre symptoms.
If none of the above does a darn thing to help you out them maybe the battery itself is toast.