If your shredder is a small personal shredder that sits on top of a waste basket. It is possible that the safety interlock is not being engaged, which will prevent the shredder from operating.
To check this, first remove the shredder head from the basket. Inside the basket there will be a small tab. If your basket is plastic, it will be a molded plastic tab that will stick out about 1/2". Metal or mesh baskets will have a small L shaped bracket that will have a 1/2" tab sticking out, on the inside of the basket.
On this style of shredder, there will be a corresponding groove, or opening that this tab will need to be aligned with. The tab slides into the groove or opening, and triggers a switch. If this switch is not engaged, the shredder will not turn on. If your unit has lights, the red and green lights will be illuminated, but you will have no reaction from the machine.****DO NOT use anything other than the basket to engage the safety switch. Improperly engaging this switch can result in injury.****
Shredders with Pull Out Drawer
Shredders with a pull out drawer for a waste bin, have a similar safety feature. The drawer will have a protruding molded plastic tab somewhere on the drawer (usually on the right hand side of the drawer) that will slide into a corresponding groove, or opening on the bottom side of the shredder head. Inside the groove or opening, there is a safety interlock switch that must be engaged in order for your unit to work. Please be sure that the basket and this groove are aligning properly or that the tab is not broken or bent