Not too clear about the details of your issue, but......if the engine stays running when you operate the deck engagement lever.......do the following checks.
With the engine not running, you need to watch how the links move above the deck when you operate the deck engagement lever on the dash.
The "hair clip" that connects the engagement link from the dash to the engagement link on the deck might have come out, letting the 2 links separate from each other.
If the engagement links are connected together, but the deck does not want to turn, you might have a locked up pulley bearing or the blade brake may be holding everything from turning.
If the deck is locked up from turning, you should hear the engine labor and maybe the belt squeal/smoke when you try to engage.
As to another version of what your problem might be:
Your opening statement sort of implies (but you don't say) that the engine might be dying when you try to engage the blades.
If that is what you are experiencing, your seat switch is defective or out of adjustment, or unplugged.
The "engine killing" safety interlock on this tractor is limited to the operation of the deck only. The clutch/brake switch on this model only affects the starting circuit.
If your engine dies when you engage the deck, it is because the seat switch "thinks" the seat is not occupied when the deck safety switch closes its portion of that circuit.
And because the seat switch connector has a "shorting shunt" built into it, unplugging the connector from the switch has exactly the same effect as an unoccupied seat, and will also stop the engine when the deck switch closes.

As always, thanks for your help. The engine continues to run when I engage the blades. The engine has a hesitation in it when I push the throttle all the way in. But this happens even when I'm not engaging the blades. So I pull the throttle out a little and the engine runs a full speed. i didn't think this had anything to do with the blades not engaging so i didn't mention. I will check the links and pulleys as you instructed and report back.

You are correct in that the slight engine hesitation has nothing to do with the blade problem. That hesitation is only the slight lag time it takes for the governor to adapt to the change of throttle opening when you call for more RPM, and the natural "leaning out" effect of those actions on carburetion.

"The engine continues to run when I engage the blades."

Then you have a purely mechanical issue.
Belt too loose, or clutch idler not moving far enough to tighten the blade belt sufficiently.

Owners manual at the link if you don't have one.

Here is a link that might be useful: Owners Manual

As always, thanks for all your help.

IâÂÂll use the mower deck diagram from the manual to explain what I have done and observed to try and get the blades to engage. I checked all the pulleys and all have movement as well as the blades. Also, all hair clips seem to be in place.

ÃÂ I observed the links above the deck while the engagement level was moved up and down. I noticed that there was no movement in the Rod Pivot (#41) and Rod, Clutch, Secondary (#43). I also notice there is not tension on belt when the level is engaged.

I removed the deck from the tractor and changed the deck belt. ÃÂ When put the deck back on I noticed that there is still no tension on the belt.ÃÂ From my observation, it appears that the rod clutch secondary (#43) goes into a plate that should move the pulley forward when the level is engaged. This is not happening. I used a large screwdriver to move the plate forward. I sprayed with wd 40 to see if it would get it moving. No happenings. Put the deck back on and engine pulley is turning but no tension on the deck belt and no movement with the rod pivot or the rod clutch.

Perhaps you could post a photo or two of the deck while it is out of the tractor.
Maybe place a paper tag on rod # 43 to identify it in the pic.
Did you have the deck off of the tractor just before the non-engagement issue showed up? Or did this just happen "out of the blue"?
I ask because in applications where the deck belt has to be "drawn tight" by a pulley to engage the blades, any "mis-mounting or mis-spacing (are those words?) of the deck attachment hardware can have a significant effect on deck performance.
I'm counting on tomplum to chime in because he might have had his hands on a Craftsman with similar linkage at some point.

I will post pictures this evening.

I did not have the deck off before noticing the problem.

I noticed this after getting the mower back from being serviced. The engine stop working but the blades were working fine. When I got it back from the shop the blades would not engage. I should have taken it back to the shop but I just didn't want to give them anymore of my money.

***"I noticed this after getting the mower back from being serviced."***
Oh dear! What was the reason for taking the tractor to the shop?
Though I had not anticipated this to be your response, it pretty well covers the same concerns I had about something being put back differently than before....if the deck had been removed prior to the non-engagement problem.
So, basically, you have dropped the deck and put it back exactly like it was AFTER it came home from the shop?
Plot is thickening.

I would take from your description that linkage is unable to move the idler cam. There can be two causes for this. One, it is simply stuck at the center where the idler cam pivots. A 9/16" deepwell socket and off the nut comes. LIft up on the pulley to hold the square head of the carriage bolt in the mounting hole so it doesn't spin. There the parts can be cleaned up, rust removed, lightly lubed and reassembled-provided they are not badly worn. Wear is easy to see here as the hole in idler cam will get egg shaped, same with the stepped washer. The hardened steel washer will just rust and not be smooth. Just about any servicing dealer keeps these in stock- and they are cheap BTW. The other issue that keeps an idler cam from engaging is excessive wear on the outer edge of the idler cam itself where the roller of the brake arms rest. If you see a divot, it is worn. You can also test this theory by moving the arm away from the cam to see if it works easier. A light lube can be used in the roller on the brake arm itself.
Two other things to check on this deck in regards to belt tension are: 1) Verify that you don't have a cracked / broken leg on one of the spindles or that a weld has not let go at the rear to the flat top plate on the deck. This is the plate where idler arm mounts to. There, that should keep you out of trouble...

I now have blades in motion. Thanks for all your help. I followed tomplum's instructions and removed the pivot plate off an cleaned all the buildup, and rust from the plate, deck and washer. The plate now pivots as it should and puts tension on the belt. Blades are now working and I don't have to rake leaves this weekend. Thanks again.