Washer does not agitate

The washer runs through all the cycles properly, with one exception, the washer does not agitate. The tub spins in the opposite direction of the spin cycle when on the wash cycle. The outter tub has a slight leak during the wash cycle. I’ve tried all of the different setting on the washer with the same result. My process of elimination to date is as follows; the belts are fine, I installed a new pump that is working properly. I have the agitator off… What should I do next and what is the correct order of process for trouble shooting this problem? Single mom of three here, so I really need to repair this machine asap, the laundry piles up fast! Thank you for any and all help!!! (Washer is approximately 13 years old, not 1 year, my mistake.)