How do i drop mower deck.

Perhaps i am wrong, i read the question several times and you had said "when i go to lower the pto engage lever" it led me to believe the blades engage manually, and your mower does not have an electric PTO. But the above answers are aimed at an electric pto.
If your blades are only engaging at certain deck heights i would speculate you simply need a deck belt, the one you have is stretched out. Some models, have a cable adjustment at the end of blade engagement cable on deck end. The small bracket the cable locks into is bolted to deck, if you loosen those bolts and pull bracket toward the outer edge of deck to provide more tension, it might take care of the issue for you.
Easy peasy. Hope this helps

Need slap out cable. On side of deck loose bolts

With the mower turned off and the deck at its lowest setting, check the top of the deck for any debris like rocks or sticks. Then watch the top of the deck while you move the engage lever. If nothing is moving, you either need to adjust the cable, reattach the cable, or install a new cable. If you see the lever with the pulley on it moving, when the engage lever is locked on, check the tightness of the belt. If it's loose, that is your problem and it could be a stretched belt.

sounds like wrong belt you raise it belts tighter lower belts looser or the tensioner has come loose

I had a similar problem with my LT1000 after the winter: engine started and ran but the blades wouldn't engage.

You need to drop the deck.
There are about 7 cotter pins holding it in place. It will help first to lower the deck, then to raise it after releasing the cotter pins. Then you can slide it out to the side.

Take a picture of the belt and pulleys running from the crankshaft under the motor and the path around the pulleys.

This will be a good chance to sharpen or replace the blades.
Check that the pulleys and blade spindles spin well.

Take more pictures for reassembly.

There are four springs which give resistance while engaging the blades, another that counteracts to release the blades and engage the brakes on the blades, and then a spring on each of the brakes. Check that everything slides well. Disassemble, clean rust and lubricate as necessary. In my case there was rust here and there that needed to be cleaned before the pieces would slide. Spent some time scraping and lubricating - plus running to get a new spring at the hardware store, before getting back into action.

As others have pointed out, check the seat spring and the actual cable to the clutch. The hardest part may just be figuring out how to drop the deck. Good luck.

This was a hand-me-down mower that hadn't received use in a couple of years.

If your blades won't engage when you raise the lever to engage them AND that lever moves freely without the normally expected resistance, then you've lost the cotter pin that connects the lever rod to the mower deck assembly. Very easy fix! Using the mower deck raise/lower lever, lower the mower deck to "down" position. Now, lay on your side along the right side of the mower and look up (use a flashlight) under the mower at the top of the mower deck while moving the blade engagement lever "up" (which pushes the connected rod down). At the end of the rod, you will see a hole where the mower deck and rod connect. Align the hole at the end of the rod with the matching "pin" on the mower deck (you'll see it) and insert a new cotter pin to secure them together. Use a nail if you don't have a cotter pin. Voila! you are done. The blade engagement lever will now engage/disengage your mower blades successfully. Just remember that mower deck must be down, or lowered, before you engage the blades!

When you move the lever and engage the blades you are also engaging the belt that drives the blades and sits on top of the mowing deck. Chances are that belt either came off one or more rollers, or broke. The only way to check it out is to get down and look on the top of the mowing deck. Get back and let me know what you find.

YOU MAY HAVE A BENT BLADE OR EXESSEIVE BUILD UP UNDER THE DECK

Try pulling on the cable coming down to deck. This cable might be your problem. Also check that the spring on the end of this cable is present and functional.