Carftsman DGT 4000 with Kohler 27hp engine suddenly stopped cutting. I cleared all of the excess grass away from the belts. Mower starts and runs very well but will not engage the blades. Please help

When you try to engage the blades have someone look under the engine to see if the drive belt does engage ( watch your fingers when looking). It is either slipping or more likely broken. I'd start here but this isn't your situation just write back and we'll go step by step.

With the motor not running have someone engage the blades as you are looking under the
Mower to see what is taking place. Don't look at the blades, look just above them where all of the pullies are. Look for a idler pully to move and tighten the belt as your friend engages the blades. It is possible that the belt has come off one of the pullies and you just can not tell it, each pully has a little post sticking up to keep the belt in place but sometimes the belt will get forced off and then will not turn the blades.

If this doesn't help give us more info.