Why does MTD yard machine Y2500 engine runs, spinner doesn't spin?

Replace belt

I'm assuming you have a Tecumseh engine on there. But a Briggs would be the same. This is straight from Tecumseh, though (long story short is run 5W30 Oil or 0W30 Synthetic in it assuming winter temperatures:

The spark plug insulation may be breaking down when hot or there is a fuel flow problem.
Try a new plug and if doesn't work have a look at these engine starting tips:

http://www.fixya.com/support/r9118692-lawnmower_not_starting

If the engine doesn't have a sump and oil filler cap, it is 2 stroke.

when the choke is fully closed your choking the fuel out,, thats why when you give i t gas it dies , its not supposed to run with the choke on and getting fuel , use the choke only until the motor warms up to operating temp,, then open it,, and you should be fine,

Check the adjustment on the gear shift it may have moved like mine did.

The operator presence bail must be in the run position to release the flywheel brake. If you can't pull the rope with the bail in the run position, your rope is fouled. You will have to remove the shroud and take it to a repair shop.

the drain plug should be on the side of the engine down near the bottom. They usually have a square head on them.

All engine makers use 30 weight oil in their engines except for kohler...they use 10W30.

if this model has a fill tube on it- turn the unit on its side to drain.