Electronic – What chemicals cause the burnt silicon / IC smell?

They are pretty susceptible to static, so I'd try a couple more.
Obviously make very sure you have it the right way round.
If they are cheap e.g. eBay parts (or from anywhere - we got sent the wrong part just last week from Farnell) then check they are not actually PNP parts (the fact that it turns off when you connect the gate to the positive supply sounds suspicious)
Also try and check that they are real parts - see if you can measure any conductance between drain and source or gate and source.

There is nothing in your circuit that should age while in storage.

In fact, those components would typically have a very long life even under load.

Some components, such as batteries and capacitors, can age while being stored, especially if stored in a hot location.

The lubricant in the motors would age slightly, the metal might corrode in an aggressive environemnt, and dirt could aggregate in the moving parts, but unless they've been stored in an extremely aggressive environment, the answer to your question is simply no, a circuit doesn't stop working just because it hasn't been used for a long time, not even the motors.