Most routers use a rocker switch (either sealed or exposed) to turn the router on and off. Over time, these rocker switches can become damaged internally, and need to be replaced. A replacement switch seldom costs more than a few dollars, and the process of replacing the switch is typically very simple.
The Bosch 1617EVS router shown in the image above has the switch located just beneath a removable housing on top of the motor. The housing is held in place with a pair of Torx screws through the top. After removing the screws, lift the top straight up and off, revealing the electrical connections above the motor.
Next, trace the two wires from the switch to their ends with spade connectors. Using a pair of needlenose pliers, lift the two spades lugs off of their spade connections. Then, using a screwdriver, push in the locks on each side of the switch (inside the motor housing) and ease the switch out of the housing. Slip the two wires out of any guide channels holding the wires in place and remove the switch.
Insert the new switch into the housing, and guide the two wires back into the same positions where the old wires were located. Attach the two spade connectors to their spades, and place the wires into the guide channels. Replace the motor housing and tighten the screws holding the housing in place.
Plug the router into power, and test the switch. If it doesn't work, re-open the housing, and verify that the spade connectors are securely connected to their spades.
NOTE: When working on any electric-powered tool, always unplug the tool from power before beginning to do any work on the tool.